FP.03: Time Value of Money

Dan has $527,432 in his 401(k) retirement fund. Assuming that the fund will generate an annual rate of return of 9%, how much must he deposit at the end of each month, in order to reach his goal of $4,000,000 in 20 years?

$1,243.60 PV = ($527,432) FV = $4,000,000 n = 240 [20 x 12] i = 9 P/YR = 12 END Mode *PMT = $1,243.60

If Steve invested $250 per month, starting a the end of each month, as a way to save for his retirement, what will he have in 40 years if he was able to receive an average of 11% return during those years?

$2,150,031.80 PMT = ($250) n = 480 [40 x 12] i = 11 P/YR = 12 END Mode *FV = $2,150,031.80

Bob Jones currently has a monthly mortgage payment of $1,656.61. He borrowed $300,000 5 years ago with loan terms of 30 years at 5.25%, and has a principal balance of $276,448.51 remaining. How much would Bob need to pay each month (starting next month) if he would like to retire this loan in 15 more years?

$2,222.31 n = 180 [15 x 12] PV = $276,448.51 i = 5.25 P/YR = 12 END Mode *PMT = ($2,222.31)

Susan and Dan feel they can afford a monthly mortgage payment of $2,800 per month. This amount would be available for principal and interest and would not include home owners insurance or property taxes. If interest rates for 15 year loans are currently 5.75%, what is the maximum amount they could borrow?

$337,182.80 n = 180 [15 x 12] i = 5.75 PMT = ($2,800) P/YR = 12 END Mode *PV = $337,182.80

Assume the following information: - Term is 5 years (n = 5) - Inflation is 3.5% - Rate of return is 9%. - The inflation adjusted return is 5.314 calculated as: 1.09 / 1.035 − 1 × 100 (i = 5.314) - Future value needed is $200,000 What is the first payment? BONUS: What is the second payment?

$37,227.55 n = 5 i = 5.314 FV = $200,000 P/YR = 1 END Mode *PMT = ($35,968.65) x 1.035 = ($37,227.55) BONUS: $38,530.52. The second payment is $37,227.55 (first payment) × 1.035 = $38,530.52

John needs $100,000 in 5 years to begin his business. He has already $30,200 saved toward this goal. If John plans to make regularly recurring quarterly deposits of $2,250 starting today, what annual rate of return must John earn to accomplish his goal?

7.83% n = 20 (5 x 4) FV = $100,000 PV = ($30,200) PMT = ($2,250) P/YR = 4 BEGIN Mode *i = 7.8

The difference between an annuity due and an ordinary annuity is?

ANNUITY DUE PAYMENTS (immediate annuity) are paid in the beginning of the period while ORDINARY ANNUITY PAYMENTS are paid at the end of the period. The difference comes out in the number used for compounding frequency.

Susan has just been notified that she will be receiving $25,000, six years from today. Susan has the opportunity to invest her funds at 7.00%, compounded semi-annually. What is the equivalent present value of she were to received this sum today? Choose the best answer. a. $16,544.58 b. $16,461.86 c. $16,379.13 d. $16,296.41

a. FV = ($25,000) n = 12 [6 x 2] i = 7 BEGIN Mode P/YR = 2 *PV = $16,544.58

What is the future value (FV) of a $10,000 lump sum invested for 5 years earning an interest rate of 10% per year, compounded quarterly?

$16,386.16 PV = ($10,000) n = 20 (5 x 4) i = 10 P/YR = 4 END Mode *FV = $16,386.16

Brenda is the beneficiary of a trust. Starting next month, she will receive monthly payments of $1,000, and this will continue for 10 years. Additionally, in 10 years time she will also receive a lump sum pay out from the trust of $100,000. If Brenda can earn 7% on her investments over the next 10 years, what is the present value of these trust payments?

$135,885.98 PMT = $1,000 n = 120 [10 x 12] FV = $100,000 i = 7 P/YR = 12 END Mode *PV = ($135,885.98)

Roy and Helen just bought a house and borrowed $340,000. The terms of the mortgage are 30 years with a fixed rate of 6%. How much will their monthly payment be at the end of each month?

$2,038.47 PV = $340,000 n = 360 (30 x 12) i = 6 P/YR = 12 END Mode *PMT = ($2,038.47)

Assume you receive $25,000, starting today, each year for the next 10 years and the inflation rate is 5% and your return on an investment is 8% over this period of time. What is the present value of this investment in today's dollars?

$220,955.95 n = 10 i = 2.86 [(8 - 5 = 3) / (1.05)] PMT = $25,000 P/YR = 1 BEGIN Mode *PV = ($220,955.95)

Diane invested $200 two years ago. She has earned an average of 10% per year. What should her investment be worth today?

$242.00 PV = ($200) n = 2 i = 10 P/YR = 1 END Mode *FV = $242.00

If Joe invested $3,250 for 5 years at a rate of 6%, and his marginal tax bracket is 35%, how much would he accumulate after taxes?

$3,935.15 PV = ($3,250) n = 5 i = 3.9 [.06 x (1 - 0.35)] P/YR = 1 END Mode *FV = $3,935.15 i >>> must be adjusted to account for the marginal tax bracket, by calculating the "after-tax compounded rate) // Formula: [investment rate x (1 - marginal tax rate)]

Several months ago, Jasmine bought some furniture. She made a down payment of $500 and borrowed the rest of the purchase price from her credit union. The terms of the loan were 48 months, monthly payments of $101.45, and an annual interest rate of 10%. Today, her loan balance is $2,761.50. What was the original amount of Jasmine's loan?

$4,000 n = 48 i = 10 PMT = ($101.45) P/YR = 12 END Mode *PV = $3,999.99 > $4,000

If Jennifer invested $2,000 into a 2 year CD paying 6% and then $3,000 a year later into a 1 year CD also paying 6%, what will she have at the end of the two year period?

$5,427.20 1. $2,000 n = 2 i = 6 PV = ($2,000) P/YR = 1 END Mode FV = $2,247.20 2. $3,000 n = 1 i = 6 PV = ($3,000) P/YR = 1 END Mode FV = $3,180.00 3. $2,247.20 + $3,180.00 = $5,427.20

It has been determined that Sue and Bob will need $250,000 in 17 years to fund their one year old child's college education. If they currently have $10,000 set aside for this goal, and average an annual rate of return of 7.5% over the next 17 years, how much must they deposit into the account every month beginning today?

$519.16 n = 204 [17 x 12] FV = $250,000 PV = ($10,000) i = 7.5 P/YR = 12 BEGIN Mode *PMT = $519.16

Justin and Diane were recently divorced. Beginning at the end of the month, Justin must pay Diane $1,000 per month for the next 5 years. These payments must be indexed to inflation, which is expected to average 3.0% over the next 5 years. Justin would like to set aside an amount today in a money market yielding 4.5% that will be sufficient to fund his 5-year obligation. What amount should Justin deposit into the money market?

$57,833.78 n = 60 [5 x 12] i = 1.46 [(4.5 - 3.0 = 1.5) / (1 + 0.03 = 1.03)] PMT = ($1,000) P/YR = 12 END Mode *PV = $57,833.78 i >>> must be adjusted to reflect the "real rate of return" // Formula: [(nominal rate - inflation rate) / (1 + inflation rate)]

David plans to open an IRA and invest $4,000 per year for the next 10 years. He will make his first deposit 1 year from today. Over the next 10 years, John projects an average annual rate of return of 8.75%. How much will the IRA be worth in 10 years?

$60,051.35 PMT = ($4,000) n = 10 i = 8.75 P/YR = 1 END Mode *FV = $60,051.35

Caroline has a required return of 8%. What is the most she would be willing to pay for the stock today, given that the stock pays a quarterly dividend of $1.05 and it is anticipated that in 5 years, when she sells the stock, it will be worth $75? The first dividend will be received in 3 months.

$67.64 n = 20 [5 x 4] i = 8 PMT = $1.05 FV = $75 P/YR = 4 END Mode *PV = ($67.64)

Sheila made equal deposits into XYX growth fund at the end of each month for the last 10 years. Over the last 10 years, the fund earned an average annual rate of return of 9.45%. Today, the fund is worth $153,849.33. How much did Sheila invest into the fund at the end of each month?

$775 n = 120 [10 x 12] i = 9.45 FV = $153,849.33 P/YR = 12 END Mode *PMT = ($775)

Debbie is going to purchase a bond, which matures in 5 years with a maturity value of $1,000. In addition to receiving the full maturity value in 5 years, the bond carries a coupon that will pay Debbie $25 every 6 months, beginning in 6 months. If Debbie has an opportunity to reinvest these coupon payments at 6%, how much should she be willing to pay for the bond?

$957.35 n = 10 [5 x 2] i = 6 FV = $1,000 PMT = $25 P/YR = 2 END Mode *FV = ($957.35)

Tom has recently hired you as his financial planner. You have informed him that unless he has a minimum time horizon of at least 10 years, you do not recommend that he count on projected stock market rates of return. What would the equivalent sum of the $500,000 inheritance in 5 years time be worth today, if Tom has the opportunity to earn 3.5% from a money market fund, compounded monthly?

($419,835.43) FV = $500,000 n = 60 (5 x 12) i = 3.5 P/YR = 12 END Mode *PV = ($419,835.43)

Beginning one month from today, Jeanine will start receiving monthly alimony payments in the amount of $1,000. She is to receive these payments for 5 years or until she remarries, whichever occurs first. Jeanine has an opportunity to invest these funds in a money market account yielding 3.7%. Assuming she does not remarry first, what is the present value of her alimony settlement?

($54,700.26) PMT = $1,000 n = 60 (5 x 12) i = 3.7 P/YR = 12 END Mode *PV = ($54,700.26)

When asked by the media what Jay was going to do with his lottery winnings, Jay responded that he was going to invest the proceeds for retirement and pretend he never actually won until he retires. It is believed that Jay is the only winning lottery receipt to ever respond this way. Jay has selected an annual installment payment method over 20 years. Each payment is $640,233.47 and the first payment will be paid immediately. Jay has an opportunity to earn an annual rate of return of 5.5% over the next 20 years. What is the present value of his winnings?

($8,071,841.76) PMT = $640,233.47 n = 20 i = 5.5 P/YR = 1 BEGIN Mode *PV = ($8,071,841.76)

David invested $10,000 in a mutual fund 32 years ago. Today, that fund is worth $237,143.02. What was the annual rate of return realized?

10.40% n = 32 PV = ($10,000) FV = $237,143.02 P/YR = 1 END Mode *i = 10.40

Roy and Helen just bought a house and borrowed $340,000. The terms of the mortgage are 30 years with a fixed rate of 6%. Let's assume that Roy and Helen will commit to making monthly payments of $2,500. How many years will it take to pay off the loan?

19.08 years PV = $340,000 i = 6 PMT = ($2,500) P/YR = 12 END Mode *n = 228.46 > 229 months / 12 = 19.08 years

Several months ago, Jasmine bought some furniture. She made a down payment of $500 and borrowed the rest of the purchase price from her credit union. The terms of the loan were 48 months, monthly payments of $101.45, and an annual interest rate of 10%. Today, her loan balance is $2,761.50. How many more payments must she make until the loan is paid off?

31 months i = 10 PMT = ($101.45) PV = $2,761.50 P/YR = 12 END Mode *n = 31

$15,000 was deposited into a savings account that earns an annual rate of return of 3.8%, compounded monthly. How many years will it take for the account to be worth $50,000?

31.75 years i = 3.8 PV = ($15,000) FV = $50,000 P/YR = 12 END Mode *n = 380.80 > 391 months / 12 = 31.75 years

How many years will it take $25,000 to grow to $100,000 if the investor is going to make monthly deposits (starting at the end of this month) of $1,225 and can earn an annual rate of return of 4.35%?

4.33 years i = 4.35 PV = ($25,000) FV = $100,000 PMT = ($1,225) P/YR = 12 END Mode *n = 51.92 = 52 months / 12 = 4.33 years

How many years will it take for $31,573 to grow to $40,000 if the investment has a rate of return of 3.5%, compounded monthly?

6.83 years PV = ($31,573) FV = $40,000 i = 3.5 P/YR = 12 END Mode *n = 81.23 > 82 months / 12 = 6.83 years

Johanna currently has an IRA with a balance of $42,504. She plans to make $4,000 deposits every year for the next 20 years. Calculate the value of the account in 20 years under the following scenarios: 1. She is able to earn an average rate of return of 8% 2. She is able to earn an average rate of return of 10% For each scenario, calculate the difference in future value for an annuity due and an ordinary annuity.

8%, Annuity Due: $395,801.01 8%, Ordinary Annuity: $381,157.18 10%, Annuity Due: $537,955.66 10%, Ordinary Annuity: $515,045.66 1. 8% rate of return Annuity Due n = 20 i = 8 PMT = ($4,000) PV = ($42,504) P/YR = 1 BEGIN Mode *FV = $395,801.01 Ordinary Annuity n = 20 i = 8 PMT = ($4,000) PV = ($42,504) P/YR = 1 END Mode *FV = $381,157.18 2. 10% rate of return Annuity Due n = 20 i = 10 PMT = ($4,000) PV = ($42,504) P/YR = 1 BEGIN Mode *FV = $537,955.66 Ordinary Annuity n = 20 i = 10 PMT = ($4,000) PV = ($42,504) P/YR = 1 END Mode *FV = $515,045.66

12 years ago, Susan initially invested $15,000 into the GHI balanced fund. Additionally, at the end of each month for the past 12 years, she made $525 deposits into the fund. If the fund is now worth $168,005.68, how much was her annual rate of return?

8.20% n = 144 [12 x 12] PMT = ($525) PV = ($15,000) FV = $168,005.68 P/YR = 12 END Mode *i = 8.20

Mary would like to know what annual rate of return she must earn in order for $20,000 invested today to grow to $50,000 in 10 years.

9.6% PV = ($20,000) n = 10 FV = $50,000 P/YR = 1 END Mode *i = 9.6%

Bob won $10 million in the lottery. He can receive 25 equal payments of $400,000 or he has the option of receiving a $5,000,000 immediate lump sum. Bob believes he can earn a return of 7% on his investments. Not taking into consideration tax consequences or inflation, should Bob take the lump sum or the 25 year payout, which starts at the end of each year? Also, what is the present value of the $400,000 payments for 25 years?

Bob should take the lump payment. 1. 25 Equal Payments n = 25 i = 7 PMT = $400,000 P/YR = 1 END Mode *PV = $4,661,433 2. Lump Sum *PV = $5,000,000

John is evaluating a capital spending project that will increase production efficiency for XYZ Company. The project will cost $285,000 and must be committed to the project today. XYZ's cost of capital is 9%. The project will save, net of taxes, $54,000 per year for 5 consecutive years and these savings will start to be realized one year from today. Additionally, at the end of year 5, it is anticipated that the equipment can be sold, net of taxes and transaction costs, for $150,000. Should XYZ make this investment?

Yes, they should make the investment. They will accumulate approx. $22,530.88 in wealth over this project. n = 5 i = 9 FV = $150,000 PMT = $54,000 P/YR = 1 END Mode *PV = ($307,530.88) > [$307,530.88 - $285,000 = $22,530.88

Roy has offered his soon to be ex-wife Samantha three alternatives of alimony payment. - Option A - $78,000 in cash, paid today. - Option B - $29,000 per year for three years, with the first payment to be paid today. - Option C - $30,000 per year for three years, with the first payment to be paid one year from today. Roy has a very successful track record for his investments and he feels he has the opportunity to earn an average of 12% per year over the next 3 years. Which option makes the most sense for Roy? Choose the best answer. a. Option C, it has the lowest PV of $72,055 b. Option A, neglecting TVM concepts, $78,000 in cash is better than either 87,000 or $90,000 c. Option A, it has the lowest PV of $78,000 d. Option B, it has the lowest PV of $77,011

a. Option A: *PV = $78,000 Option B: PMT = ($29,000) n = 3 i = 8 P/YR = BEGIN Mode *PV = $80,714.68 Option C: PMT = ($30,000) n = 3 i = 8 P/YR = 1 END Mode *PV = $77,312.91 Option A has a PV of $78,000, Option B has a PV of $78,011.48 and Option C has a PV of $72,054.94. Option C is the best for Roy. Neglecting TVM concepts never makes any sense.

Dan is considering buying an apartment building for $3.2 million. The building will generate the following after-tax cash flows: - Year 1 $26,000 - Year 2 $20,000 - Years 3-6 $31,000 - Year 7 $35,000 Furthermore, it is anticipated that Dan can sell this building for $4.3 million in 7 years, net of taxes and transaction costs. Dan has an after-tax opportunity rate of 5%. Calculate the IRR and NPV of this investment opportunity. Choose the best answer. a. IRR of 5.11% and NPV of $23,410.79 b. IRR of 5.16% and NPV of $23,410.79 c. IRR of 5.16% and NPV of $23,644.90 d. IRR of 5.11% and NPV of $23,644.90

a. TVM >>> CFLO >>> SHIFT >>> INPUT >>> CLEAR LIST? >>> YES FLOW (0): ($3,200,000) >>> INPUT >>> FLOW (1): $26,000 >>> INPUT >>> FLOW (2): $20,000 >>> INPUT >>> FLOW (3): $31,000 >>> INPUT >>> FLOW (4): $31,000 >>> INPUT >>> FLOW (5): $31,000 >>> INPUT >>> FLOW (6): $31,000 >>> INPUT >>> FLOW (7): $4,335,000 ($4,300,000 +$35,000) >>> INPUT >>> EXIT >>> CALC >>> i = 5% *NPV = $23,410.79 *IRR% = 5.11%

The nominal rate is 7% and the inflation rate is 3%. What is the real rate of return? Choose the best answer. a. 3.88% b. 3.90% c. 3.86% d. 3.84%

a. [(7 - 3) / (1 + .03)] > [(4) / (1/03)] = 3.88%

Ayn R. wants to give her daughter $25,000,000 to start her own energy company in 15 years. How much would Ayn have to invest at the beginning of each month, to achieve her goal of amassing $25,000,000 in 15 years? Assume her investments earn an annual interest rate of 8.0% compounded monthly. Choose the best answer. a. $71,767.90 b. $72,246.35 c. $71,044.65 d. $76,728.22

a. n = 180 [15 x 12] i = 8 FV = $25,000,000 BEGIN Mode P/YR = 12 *PMT = ($71,767.90)

Roger has won the Arkansas state lottery and will receive $50 at the end of each of the next 20 years. Assuming he could earn 6.0% compounded annually on his investments, what is the present value of this stream of income? Choose the best answer. a. $573.50 b. $1000.00 c. $581.59 d. $0.13

a. n = 20 i = 6 PMT = ($50) END Mode P/YR = 12 *PV = $573.50

Steve wants to begin a business in six years. He needs to have $60,000 (in today's dollars) to begin the business. Inflation is expected to average 3.5% over the next six years and Steve's investment projections show that he can earn 5.5% on his investments over this time horizon. What serial payment should Steve deposit at the end of the first and second years? Choose the best answer. a. $9,861.16, $10,206.30 b. $9,718.24, $9,912.60 c. $9,527.69, $9,718.24

a. n = 6 i = 1.93 [(5.5 - 3.5 = 2) / (1 + 0.035 = 1.035)] FV = $60,000 END Mode P/YR = 1 *PMT = ($9,527.69) - End of First Year: 9,527.69 x 1.035 = $9,861.16 - End of Second Year: 9,861.16 x 1.035 = $10,206.30

Midge wants to accumulate $100,000 for a down payment on a home in 5 years. She currently has $25,000 saved and she can invest $750 at the beginning of every month for the next 5 years. She expects to earn an 11% annual rate compounded monthly on her investments. Will she be able to attain her goal? Choose the best answer. a. Yes. b. No. c. Cannot be determined.

a. n = 60 [5 x 12] i = 11 PV = ($25,000) PMT = ($750) BEGIN Mode P/YR = 12 *FV = $103,408.14

On June 1st, Donna lent a friend $25,000. The term of the loan is for 6.5 years, and carries an annual interest rate of 8.25%. The first monthly payment payable to Donna is due on July 1st, and the will be due the first of each month thereafter. How much are the monthly payments Donna will receive? Choose the best answer. a. $415.17 b. $417.25 c. $419.32 d. $421.40

a. n = 78 [6.5 x 12] i = 8.25 PV = ($25,000) P/YR = 12 END Mode *PMT = ($415.17)

Jason feels that the lump sum available from his 401(k) investment needs to be $1,000,000 when he turns 65, which is in 7 years. If Jason does not plan to make any other contributions into the plan, how much of a lump sum does Jason need today in order to grow to $1,000,000 when he retires in 7 years? Assume that Jason can earn an average of 9% per year on this investment over the 7 year time horizon. Choose the best answer. a. $602,451 b. $547,034 c. $602,451 d. $623,874

b. FV = $1,000,000 n = 7 i = 9 P/YR = 1 END Mode *PV = $547,034

Eileen sustained bodily injury as well as pain and suffering 5.5 years ago while at work. She promptly sued her employer 5.5 years ago and was finally awarded $220,000 in damages today. Eileen had the opportunity to earn 4.4% in a money market fund, compounded monthly over the last 5.5 years. What was the present value of her eventual settlement at the time she initiated the lawsuit? Choose the best answer. a. $171,145.63 b. $172,788.82 c. $173,457.38 d. $174,956.37

b. FV = $220,000 n = 66 (5.5 x 12) i = 4.4 P/YR = 12 END Mode *PV = $172,788.82

$20,000 was deposited into a savings account that earns an annual rate of return of 3.7%, compounded monthly. How many years will it take for the account to be worth $50,000? Choose the best answer. a. 24.92 years b. 24.83 years c. 24.75 years d. 24.50 years

b. PV = ($20,000) FV = $50,000 i = 3.7 END Mode P/YR = 12 *n = 297.63 / 12 = 24.83

Grace needs to set a lump sum aside today that will generate the following future cash flows, in today's dollars, needed for her daughter's college tuition: - Now: $0 - Years 1 - 8: $0 - Years 9 - 12: $30,000 The college rate of inflation is 6%, and Grace as an opportunity to invest her funds at 8%. How much does Grace need to set aside today in order to fund her daughter's education? Choose the best answer. a. $97,650.26 b. $98,636.63 c. $98,143.45 d. $97,157.08

b. STEP 1: Find College Cost/Year (with Inflation) -Freshman Year: n = 9 i = 6% PV = ($30,000) P/YR = 1 BEGIN Mode *FV = $50,684.37 - Sophomore Year: n = 10 *FV= $53,725.43 - Junior Year: n = 11 *FV = $56,948.96 - Senior Year: n = 12 *FV = $60,365.89 TOTAL: $221,724.66 in today's dollars STEP 2: Input into CFLO TVM >>> CFLO >>> SHIFT >>> INPUT >>> CLEAR LIST? >>> YES FLOW (0): $0 >>> INPUT >>> FLOW (1): $0 >>> INPUT >>> FLOW (2): $0 >>> INPUT >>> FLOW (3): $0 >>> INPUT >>> FLOW (4): $0 >>> INPUT >>> FLOW (5): $0 >>> INPUT >>> FLOW (6): $0 >>> INPUT >>> FLOW (7): $0 >>> INPUT >>> FLOW (8): $0 >>> INPUT >>> FLOW (9): $50,684.37 >>> INPUT >>> FLOW (10): $53,725.43 >>> INPUT >>> FLOW (11): $56,948.96 >>> INPUT >>> FLOW (12): $60,365.89 >>> INPUT >>> EXIT >>> CALC >>> i = 8% *NPV = $98,636.63

David has begun making $1,000 monthly alimony payments to his ex-wife Sheila. Sheila received the first payment today and she expects to receive these payments for the full 10 years as defined in the divorce decree. If Sheila has the opportunity to earn 7% on her money over the next ten years, what is the present value of this payment stream? Choose the best answer. a. $87,495.05 b. $86,628.76 c. $86,195.62 d. $87,061.90

b. n = 120 [10 x 12] i = 7 BEGIN Mode P/YR = 12 PMT = ($1,000) *PV = $86,628.76

Dana invested $10,000 in a mutual fund 35 years ago. Today, that fund is worth $329,366.73. What was the annual rate of return realized? Choose the best answer. a. 10.75% b. 10.00% c. 10.50% d. 10.25%

c. FV = $329,366.73 PV = ($10,000) n = 35 END Mode P/YR = 1 *i = 10.50

Samantha has the opportunity to invest funds at 8% per year over the next three years. She has to decide which option to select among three alternatives of alimony payment from her soon to be ex-husband, Roy. - Option A - $78,000 in cash, received today. - Option B - $29,000 per year for three years, with the first payment to be received today. - Option C - $30,000 per year for three years, with the first payment to be received one year from today. Which option should she select, and why? Choose the best answer. a. Option C, it has the highest PV of $81,313 b. Option C, neglecting TVM concepts, $90,000 in cash is better than either $87,000 or $78,000 c. Option B, it has the highest PV of $80,715 d. Option A, it has the highest PV of $78,000

c. Option A: *PV = $78,000 Option B: PMT = ($29,000) n = 3 i = 8 P/YR = BEGIN Mode *PV = $80,714.68 Option C: PMT = ($30,000) n = 3 i = 8 P/YR = 1 END Mode *PV = $77,312.91 While the PV of option B is $80,714.68, the correct PV of Option C is $77,312.91. Although Option A is in fact better than Option C, Option B is the best with the highest present value. Neglecting TVM concepts never makes any sense.

Nancy has just entered into a contract that requires her client to make quarterly payments of $825 over the next 7 years. Nancy can invest these funds over the next 7 years at 5.6%, compounded quarterly. How much is the present value of this contract, if the first payment begins 3 months from today?. Choose the best answer. a. $20,145.18 b. $18,587.23 c. $19,001.89 d. $19,786.54

c. PMT = $825 n = 28 (7 x 4) i = 5.6 P/YR = 4 END Mode *PV = $19,001.89

A small cap mutual fund is expected to earn an average annual rate of 12.5% over the next 10 years. If Julie invests $10,000 today, how much should she expect the fund to grow to in 10 years? Choose the best answer. a. $22,142 b. $31,791 c. $32,473 d. $33,568

c. PV = $10,000 n = 10 i = 12.5 P/YR = 1 END Mode *FV = $32,473

Dan can earn 9% on his investments, although prevailing inflation rate is 4%. What is the nominal and real rate of return on his investments? Choose the best answer. a. Nominal = 5.00%, Real = 4.00% b. Nominal = 4.81%, Real = 4.19% c. Nominal = 9.00%, Real = 4.81% d. Nominal = 4.00%, Real = 5.00%

c. The nominal rate (9.00%) is the total rate that he can earn. The real rate (or inflation adjusted) is the rate that he can earn while preserving purchasing power. The formula is [(Nominal rate - inflation rate) ÷ (1 + inflation rate)]. Therefore: (9 - 4) ÷ 1.04 = 4.81%.

Assume Mary purchased a condo on July 1st of this year using a 30-year $175,000 mortgage at 4.50%. For the timely mortgage payments Mary made this year, what amount of interest will she report as an itemized deduction on her income tax return IRS Form 1040? Choose the best answer. a. $1,396 b. $2,823 c. $3,924 d. $7,817

c. n = 360 [30 x 12] i = 4.5 PV = $175,000 P/YR = 12 END Mode *PMT = ($886.70) OTHER >>> AMRT >>> 6 >>> #P >>> ($3,924.48) - 6 because the condo was purchased on July 1st of the year, and so only 6 payments were made.

George was given the opportunity to invest in an investment that will pay $1,000 a year from now and another $2,000 two years from now. The investment requires George to invest $2,500 now. He can earn 10% per year on his money by leaving it in the bank. Which of the following statements are true? Choose all that apply. a. The bank is the better alternative. b. The NPV of the investment is negative. c. The NPV of the investment is positive. d. The investment is the better alternative.

c. + d. PV of bank account = 1000/(1.1) + 2000/(1.1)2 = $2,562. It would take $2,562 at the bank to generate the same future cash flows that the $2,500 PV investment would generate. Because the outlay required on the project is only $2,500, it has a net present value of $2,562 - $2,500 = $62. An investment with a positive NPV should be undertaken.

Jason is 20 years old and has just been offered an opportunity to invest in his employer's 401(k) plan. Jason has determined that he can contribute $500 per month starting next month. Jason is reviewing three different mutual funds. Fund A is an income fund with a historical rate of return of 6%. Fund B is a balanced fund with a historical rate of return of 9%. Fund C is an aggressive growth fund that has historically generated a 12% return. Projecting these historical rates of return into the future for each fund, what will be the value of Jason's 401(k) in 47 years, when Jason is 67 years old? (Round all calculations to the dollar). Choose the best answer. a. (A) $1,558,108, (B) $4,420,529, (C) $13,566,198 b. (A) $1,558,108, (B) $4,442,743, (C) $13,566,198 c. (A) $1,565,938, (B) $4,420,529, (C) $13,634,370 d. (A) $1,565,938, (B) $4,442,743, (C) $13,634,370

d. Fund A: n = 564 [47 x 12] i = 6 PMT = ($500) P/YR = 12 END Mode *FV = $1,565,928 Fund B: n = 564 [47 x 12] i = 9 PMT + ($500) P/YR = 12 END Mode *FV = $4,442,743 Fund C: n = 564 [47 x 12] i = 12 PMT + ($500) P/YR = 12 END Mode *FV = $13,634,370

John is 16 years old and recently started working. He plans to invest $4,000 per year into an IRA for the next 50 years, and he has just made his initial investment of $4,000 today. Assuming John can earn long-term stock market returns of 10%, how much will his IRA be worth when John is 66 years old? Choose the best answer. a. $1,005,623.26 b. $1,549,711.33 c. $3,423,152.79 d. $5,121,197.53

d. PMT = ($4,000) n = 50 i = 10 P/YR = 1 BEGIN Mode *FV = $5,121,197.53

Joan has 20 years and 3 months remaining on her mortgage and the balance remaining on this loan is $226,016.26. She originally borrowed $265,000 at a fixed rate of 6.5%. The term of the loan was originally for 30 years and her scheduled monthly payment is $1,674.98. She has no prepayment penalty and she has asked you to calculate what her new payment amount would be if she decides to make monthly payments that would retire the loan over the next 180 months (15 years). She will continue to make these payments at the end of the month. Calculate her new monthly payment. Choose the best answer. a. $1,978.68 b. $1,988.53 c. $1,998.37 d. $1,968.84

d. PV = $226,016.26 n = 180 [15 x 12] i = 6.5 END Mode P/YR = 12 *PMT = ($1,968.84)

Andre has just learned that in 22 months he is being transferred overseas. He purchased his house exactly 5 years ago and borrowed an initial mortgage amount of $333,700. The term of the loan was 30 years, and carried a fixed rate of 5.75%. How much is Andre's current remaining loan balance (after 60 months) and how much will Andre's remaining balance on his mortgage be in 22 months when he is transferred? Round your answer to the dollar. Choose the best answer. a. $308,000 after 60 months, $297,312 after 82 months b. $309,548 after 60 months, $297,312 after 82 months c. $308,000 after 60 months, $298,806 after 82 months d. $309,548 after 60 months, $298,806 after 82 months

d. PV = $333,7000 n = 360 [30 x 12] i = 5.75 END Mode P/YR = 12 *PMT = ($1,947.38) - 60 months: OTHER >>> AMRT >>> 60 >>> #P >>> INT *INT = ($92,690.34) *BAL = $309,547.54 - 22 months: OTHER >>> AMRT >>> 22 >>> #P >>> INT *INT = ($32,100.94) *BAL = $298,806.12 Even though the question does not ask about interest paid, you must amortize the loan over 60 months and calculate the interest paid, as an interim step prior to recalling the present value.

Jane's parents have given her $60,000 to open up a 529 college saving plan for Jane's son David, who is currently 2 years old. If the 529 plan earns an average rate of return of 8.5% over the next 16 years, how much will be available for David's education when he is 18 years old? Choose the best answer. a. $205,556.56 b. $228,615.73 c. $207,084.50 d. $221,323.26

d. PV = ($60,000) n = 16 i = 8.5 P/YR = 1 BEGIN Mode *FV = $221,323.26

John and Debbie recently purchased a home. The inspection report revealed that the furnace will need to be replaced in 3 years, the hot water heater has an expected remaining life of 4 years, and the roof will need to be replaced in 7 years. The cost to repair these items (in today's dollars) is: - Furnace - $5,200 (needed in 3 years) - Hot water heater - $1,500 (needed in 4 years) - Roof - $8,400 (needed in 7 years) If the cost of these items is expected to increase with the general rate of inflation (3.5%), how much should John and Debbie set aside today if they can invest these funds in a money market generating a return of 5%? Choose the best answer. a. $13,921.61 b. $14,061.53 c. $14,131.49 d. $13,991.57

d. STEP 1: Find out how much these repairs cost in today's dollars - Furnace: n = 3 i = 3.5 PV = ($5,200) P/YR = 1 END Mode *V = $5,765.33 - Hot Water Heater: n = 4 i = 3.5 PV = ($1,500) P/YR = 1 END Mode *FV = $1,721.88 - Roof: n = 7 i = 3.5 PV = ($8,400) P/YR = 1 END Mode *FV = $10,687.15 STEP 2: Input these quantities into CFLO to find the NPV needed. TVM >>> CFLO >>> SHIFT >>> INPUT >>> CLEAR LIST? >>> YES FLOW (0): $0 >>> INPUT >>> FLOW (1): $0 >>> INPUT >>> FLOW (2): $0 >>> INPUT >>> FLOW (3): $5,765.33 >>> INPUT >>> FLOW (4): $1,721.88 >>> INPUT >>> FLOW (5): $0 >>> INPUT >>> FLOW (6): $0 >>> INPUT >>> FLOW (7): $10,687.15 >>> INPUT >>> EXIT >>> CALC >>> i = 5 NPV = $13,921.61

Assume you can make a $25,000 investment today that will pay an average annual after-tax cash flow of $10,000 for the next 5 years. If your opportunity cost of money is 10.0% what is the NPV of this investment? Choose the best answer. a. $50,000.00 b. $26,000.00 c. $37,907.87 d. $12,907.87 BONUS: What's the IRR on this investment? a. 10.00% b. 28.65% c. 3.00% d. -10.00%

d. TVM >>> CFLO >>> SHIFT >>> INPUT >>> CLEAR LIST? >>> YES FLOW (0): ($25,000) >>> INPUT >>> FLOW (1): $10,000 >>> INPUT >>> FLOW (2): $10,000 >>> INPUT >>> FLOW (3): $10,000 >>> INPUT >>> FLOW (4): $10,000 >>> INPUT >>> FLOW (5): $10,000 >>> INPUT >>> EXIT >>> CALC >>> i = 10.00% *NPV = $12,907.87 BONUS: b. 28.65% CALC >>> IRR% >>> *IRR% = 28.65%

Peter Lynch has been dollar-cost averaging into the Magellan Fund by investing $6,250 at the end of each quarter for the past 25 years. Assuming he has earned a 6% annual rate compounded annually, how much has Peter accumulated? Choose the best answer. a. $1,451,469.31 b. $4,331,212.27 c. $348,972.24 d. $1,430,019.02

d. n = 100 [25 x 4] i = 6 PMT = ($6,250) END Mode P/YR = 4 *FV = $1,430,019.02

Steve's aunt just died and left him $10,000. He will deposit this amount in a growth and income mutual fund that is expected to earn an annual return of 9.0% over the next 10 years. If Steve deposits an additional $500 into this mutual fund at the end of every month for the next 10 years, what will his account be worth in 10 years? Choose the best answer. a. $120,664.36 b. $120,058.00 c. $121,877.06 d. $121,270.71

d. n = 120 [10 x 12] i = 9 PV = $10,000 PMT = ($500) END Mode P/YR = 12 *FV = $121.270.71

Bob and Jerry just purchased their first house. They consider it to be a starter home as they would like to begin a family soon so they borrowed $180,000 from the local bank. The terms were a fixed rate of 6.0%, 15 years of length, and the scheduled monthly payments are $1,518.94. They have asked you to determine how much debt will remain and be payable to the bank after 3, 5, and 7 years. Please calculate the loan balance at these points in time. Choose the best answer. a, $156,431.61, $136,816.57, $116,162.44 b. $156,431.61, $136,132.49, $115,584.52 c. $155,653.34, $136,132.49, $116,162.44 d. $155,653.34, $136,816.57, $115,584.52

d. n = 180 [15 x 12] i = 6 PV = $180,000 END Mode P/YR = 12 *PMT = ($1,518.94) - 3 years balance remaining OTHER >>> AMRT >>> 36 [3 x 12] >>> #P >>> BAL *BAL = $155,653.34 - 5 years balance remaining OTHER >>> AMRT >>> 24 [2 x 12] >>> #P >>> BAL *BAL = $136,816.57 - 7 years balance remaining OTHER >>> AMRT >>> 24 [7 x 12] >>> #P >>> BAL *BAL = $115,584.52

Assume Ken purchased a home on September 1st of this year using a 30-year $375,000 mortgage at 4.70%. For the timely mortgage payments Ken made, what amount of interest will he report as an itemized deduction next year on his IRS Form 1040? Choose the best answer. a. $1,916 b. $5,864 c. $5,930 d. $17,408

d. n = 360 [30 x 12] i = 4.7 PV = $375,000 P/YR = 12 END Mode *PMT = ($1,944.89) OTHER >> AMRT >> 12 >> #P >> $17,408

Marcia wants to begin a business in seven years. She needs to have $75,000 (in today's dollars) to begin the business. Inflation is expected to average 3.0% over the next seven years and Marcia's investment projections show that she can earn 6% on her investments over this time horizon. What serial payment should Marcia make at the end of the first and second years? Choose the best answer. a. $9,862.97, $10,158.86 b. $9,813.90, $10,108.32 c. $10,158.86, $10,563.63 d. $10,108.32, $10,411.57

d. n = 7 i = 2.91 [(6 - 3) / (1 + 0.03)] FV = $75,000 P/YR = 1 END Mode *PMT = ($9,813.90) - First Year: -9,813.90 x 1.03 = $10,108.32 - Second Year: $10,108.32 x 1.03 = $10,411.57

John O. invested $1,000 in a Franklin Mint plate commemorating the Apollo space program. He estimates the plate will appreciate at a 2.0% annual rate compounded semi-annually. How much will his plate be worth at the end of 45 years? Choose the best answer. a. $2,457.76 b. $2,437.85 c. $1,218.93 d. $2,448.63

d. n = 90 [45 x 2] i = 2 PV = ($1,000) END Mode P/YR = 2 *FV = $2,448.63