Intro to Principals of Finance Test 2 math problems

What is the monthly rate if the APR is 12% with monthly compounding:

12/12=1%

You are looking at an investment that will pay $1,200 in 5 years if you invest $1,000 today. What is the implied rate of interest:

I/Y: 3.71% -N: 5 - PV -$1,000 - FV: $1,200 - CPT I/Y: 3.71%

Suppose you have $1,000 now in a savings account that is earning 6%. You want to add $500 one year from now and $700 two years from now. How much will you have two years from now in your savings account:

Year 1: $1,560 -N: 1 -PV: -$1,000 -I/Y: 6% -CPT FV: $1,060 -($1,060+$500=$1,560) Year 2: $2,354.00 -N: 1 -PV: -$1,560 -I/Y: 6% -CPT FV: $1,654 -($1,654+$700=$2,354)

Consider receiving the following cash flows: - Year 1 CF: $200 - Year 2 CF: $400 - Year 3 CF: $600 - Year 4 CF: $800 If the discount rate is 12%, what would this cash flow be worth today?

Year 1: -$178.57 Year 2: -$318.88 Year 3: -$427.07 Year 4: -$508.41 Total: -$1,432.93

Consider a 5 years, interest only loan with a 7% interest rate. The principal amount is $10,000. interest paid is annually.

year 1-4: - interest payments of 0.07*$10,000= $700 year 5: -interest+principal: $10,000+$700= $10,700

Suppose you invest the $1,000 from the previous example for 5 years at 5% how much would you have at time 5?

$1,276.28 -N: 5 -I/Y: 5.5% -PV: -$10 -CPT FV: $1,276.28

Your parents set up a trust fund for you 10 years ago that is now worth $19,671.51. If the fund earned 7% per year: how much did they invest?

-$10,000 -N: 10 - I/Y: 7% - FV: $19,671.51 - CPT PV: -$10,000

What is the present value of $500 to be received in 5 years? 10 years? The discount rate is 10%

-$310.46 (5 Years) - $192.77 (10 years) -N: 5 -I/Y: 10% -FV: $500 -CPT PV: -$310.46 -N: 10 -I/Y: 10% -FV: $500 -CPT PV: -$192.77

You want to begin saving for your daughter's college education and you estimate that she will need $150,000 in 17 years. If you feel confident that you can 8%, how much do you need to invest today:

-$40,540.34 -N: 17 - I/Y: 8% -FV: $150,000 - CPT PV: -$40,540.34

Suppose you had a relative deposit $10 at 5.5% 200 years ago

-$447,189.84 - N: 200 - I/Y: 5.5% - PV: -$10 - CPT PV: -$447,189.84

Even though most corporate bonds in the US make coupon payments semiannually, bonds issued elsewhere often have annual coupon payments. Suppose a German company issues a bond with a par value of $1,000, 25 year to maturity, and a coupon rate of 6.3% paid annually. If the yield to maturity is 7.4% what is the current price of the bond

-$876.30 -PMT: 63 -FV: $1,000 -N: 25 -CPT PV: -876.30

Suppose you need $10,000 in one year for the down payment of a new car. if you can earn 7% annually. how much do you need to invest today?

-$9,345.79 -FV: $10,000 - I/Y: 7% - N: 1 - CPT PV: -$9,345.79

What is the APR if the monthly rate is 0.5%

0.5%*12=6%

What is the APR if the semiannual rate is 0.5%

0.5%*2=.01 or 1%

Suppose you can earn 1% per month on $1 invested today: What is the APR: how much are you effectively earning:

1*12=12% FV: 1(1.01)^12=1.1268 Rate: (1.1268-1)/1= 0.1268 or 12.68%

What is the present value of $500 received in 5 years if the interest rate is 10%? 15%?

10%: -$310.46 15%: -$248.59 -N: 5 -I/Y: 10% -FV: $500 -CPT PV:-$310.46 -N: 5 -I/Y: 15% -FV: $500 -CPT PV: -$248.59

Suppose you want to earn an effective rate of 12% and you are looking at an account that compounds on a monthly basis. What APR must they pay:

11.39% To solve: -2nd Iconv down arrow 12 EFF enter down arrow 12 C/Y enter down arrow CPT NOM

Suppose you put it in another account and earn 3% per quarter: What is the APR: how much are you effectively earning

3*4=12% FV: 1(1.03)^4=1.1255 Rate:(1.1255-1)/1= 0.1255 or 12.55%

Huggins Co. has identified an investment project with the following cash flows: Year Cash flow 1 $890 2 $1,270 3 $1,530 4 $1,700 If the discount rate is 9% what is the present value of these cash flows: What is the present value at 20% What is the present value at 30%

9%: $4,271.2 - (816.51+ 1068.93+1181.44+1204.32) 20%: $3,328.86 -(741.67+881.94+885.42+819.83) 30%: $2,727.72 -(684.62+751.48+696.40+595.22)

Tai Credit Corp. wants to earn an effective annual return on its consumer loans of 14% per years. The bank uses daily compounding on its loan. What interest rate is the bank required by law to report to potential borrowers?

APR: 13.11% To solve using a calculator: -2nd Iconv C/Y: 365 EFF: 14% CPT NOM: 13.11%

Your coin collection contains 58 1952 silver dollars. If your grandparents purchased them for their face value when they were new, how much will your collection be worth when you retire in 2068, assuming they appreciate at the annual rate of 4.9%:

CPT FV: $14,906.81 -N: 2068-1952= 116 - I/Y: 4.9% -PV: $58 -CPT FV: $14,906.81

You are saving for a new house and you need 20% to get a loan. You put $10,000 per year in an account paying 8%. The first payment is made today/ How much will you have at the end of 3 years (you make a total of three $10,000 payments)

CPT FV: $35,061.12 -N: 3 -PMT: -$10,000 -I/Y: 8% -CPT FV: $35,061.12 What if it were an ordinary annuity: $32,464 How much more would you receive:$35,061.12-$32,464=$2,597.12

Suppose you begin saving for your retirement by depositing $2,000 per year in an IRA. If the interest rate is 7.5%, how much you have will in 40 years:

CPT FV: $454,513.04 -N: 40 -I/Y: 7.5% -PMT -$2,000 -CPT FV: $454,513.04

Suppose you borrow $25,000 from your parents to buy a car. You agree to pay $500 per month for 60 months. What is the monthly interest rate:

CPT I/Y: 0.62% -N: 60 -PV: $25,000 -PMT: -$500 -CPT I/Y: 0.62%

Suppose you are offered an investment that will allow you to double your money in 6 years. You have $10,000 to invest. What is the implied rate of interest?

CPT I/Y: 12.25% -N: 6 -FV: $20,000 -PV: -$10,000 -CPT I/Y: 12.25%

Suppose you have a 1 year old son and you want to provide $75,000 in 17 years towards his college education. You currently have $5,000 to invest. What interest rate must you earn to have $75,000 when you need it:

CPT I/Y: 17.27% -N: 17 -PV: -$5,000 -FV: $75,000 -CPT I/Y: 17.27%

Assume the total cost of a college education will be $200,000 when your child enters college in 16 years. You presently have $55,000 to invest. What annual rate of interest must you earn on your investment to cover the entire cost of your child's education:

CPT I/Y: 8.40% -N: 16 -FV: $200,000 -PV: -%55,000 -CPT I/Y: 8.40%

You're trying to save to buy a new $203,000 Ferrari. You have $53,000 today that can be invested at your bank. The bank pay 6.1% annual interest on its accounts. How long will it be before you have enough to buy the car?

CPT N: 22.68 years -FV: $203,000 -PV: -$53,000 -I/Y: 6.1% -CPT N: 22.68

Suppose you borrow $2,000 at 5%, and you are going to make annual payments of $734.42:

CPT N: 3 Years -PV: $2,000 -I/Y: 5% -PMT: -$734.42 -CPT N: 3

You want to purchase a new car, and you are willing to pay $20,000. if you invest at 10% per year and you currently have $15,000, how long will it be before you have enough money to pay cash for the car?

CPT N: 3.02 Years -FV: $20,000 -PV: -$15,000 -I/Y: 10% -CPT N: 3.02

One of your customers is delinquent on his account payable balance. You've mutually agreed to a repayment of $500 per month. You will charge 1.35% per month interest on the overdue balance. if the current balance is $12,500, how long will it take for the account to be paid off?

CPT N: 30.70 month -I/Y: 1.35% -PMT: $500 -PV: $12,500 -CPT NL 30.70 months

You ran a little short on your spring break vacation, so you put $1,000 on your credit card. You can only afford to make the minimum payment of $20 per month. The interest rate on the credit card is 1.5 percent per month: How long will you need to pay off the $1,000:

CPT N: 93.11 Months or 7.75 years -I/Y: 1.5% -PV: $1,000 -PMT: -$20 -CPT N: 93.11 months or 7.75 years

Suppose you have $200,000 to deposit and can earn 0.75% per month How much could you receive every month for 5 years:

CPT PMT: $4,151.67 -PV: -$200,000 -N: 60 -I/Y: 0.75% -CPT PMT: $4,151.67

DMA corporation has bonds on the market with 19.5 years to maturity, a YTM of 6.6%, and a current price of $1,043. The bonds make semi annual payments and have a par value of $1,000. What must the coupon rate be on these bonds?

CPT PMT: 34.98 -N: 39 -YTM: 6.6/2=3.3 (I/Y?) -PV: 1,043 -CPT PMT: 34.98

Imprudential, Inc. has an unfunded pension liability of $579,000,000 that must be paid in 25 years. To asses the value of the firm's stock, financial analysis want to discount this liability back to the present. If the relevant discount rate is 7.2%, what is the present value of this liability:

CPT PV: $101,814,335.20 -N: 25 -FV: $579,000,000 -I/Y: 7.2% -CPT PV: $101,814,335.20

After carefully going over your budget, you have determined you can afford to pay $632 per month towards a new sports car. You call up your local bank and find out that the going rate is 1 % per month for 48 months. How much can you borrow:

CPT PV: $23,999.54 -N: 48 -I/Y: 1% -PMT: -$632 -CPT PV: $23,999.54

Your company will generate $70,000 in annual revenue each year for the next 7 years from a new information database. If the appropriate interest rate is 8.25%, what is the present value of the savings?

CPT PV: $361,350.50 -N: 7 -I/Y: 8.25% -PMT: -$70,000 -CPT PV: $361,350.50

After carefully going over your budget, you have determined you can afford to pay $645 per month towards a new sports car. You call your local bank and find out that the going rate is 12% per year with monthly compounding for 4 years. How much can you borrow?

CPT PV: -$24,493.20 -N: 12*4=48 months -I/Y: 1% per month -PMT: -$645 -CPT PV: -$24,493.20

You want to receive $5,000 per month for the next 5 years. How much would you need to deposit today if you can earn 0.75% per month: What monthly rate would you need to earn if you only have $200,000 to deposit: Suppose you have $200,00 to deposit and can earn 0.75% per month How many months could you receive the $5,000 payment

CPT PV: -$240,867 -N: 5*12=60 -PMT: $5,000 -I/Y: 0.75% -CPT PV: -$240,867 CPT I/Y: 1.44% -PV: -$200,000 -N: 60 -PMT: $5,000 -CPT I/Y: 1.44% CPT N: 47.73 -PV: -$200,000 -I/Y: 0.75% -PMT: $5,000 -CPT N: 47.73

If a T-bill promises to repay $10,000 in 12 months and the market interest rate is 7%, how much will the bill sell for in the market

CPT PV: -$9,345.79 -N: 1 -FV: $10,000 -I/Y: 7 -CPT PV: -$9,345.79

Suppose the Fellini Company wants to sell preferred stock at $100 per share. A similar issue of preferred stock already outstanding has a price of $40 per share and offers a dividend of $1 every quarter: What dividend will Fellini have to offer if the preferred stock is going to sell:

Current Required Return: - 40=1/r -r: .025 or 2.5% per quarter - dividend for new preferred: -100=C/0.25 C= 2.50 per quarter

Lets verify the choice. Suppose you invest $100 in each account. How much will you have in each account in one year.

First Account: -N: 365 -I/Y: 5.25/365=.01439 -PV: -100 -CPT FV: $105.39 Second Account: -N:2 -I/Y: 5.3/2= 2.65 -PV: -100 -CPT FV: $105.37

You are looking at two savings accounts. One pays 5.25% with daily compounding. The other pays 5.3% with semi annual compounding. Which account should you use:

First account: - EAR: (1+.0525/365)^365-1=0.0539 Second account: -EAR: (1+0.053/2)^2-1=5.37% To solve using a calculator: - 2nd Iconv 5.25 NOM enter up arrow 365 C/Y enter up arrow CPT EFF: 5.39% - 5.3 NOM enter up arrow 2 C/Y enter up arrow CPT EFF: 5.37%

First national bank charges 13.6 compounded monthly on its business loans. First united bank charges 13.9 compounded semi annually. Calculate the EAR for First national bank and First united bank: As a potential borrower, which bank would you go to for a new loan:

First national bank: 0.1448 First united bank: 0.1438 To solve using a calculator: -2nd Iconv NOM: 13.6,13.9 C/Y: 12,2 CPT EFF: 14.48,14.38

First city bank pays 6% simple interest on its savings account balances, whereas second city bank pays 6% compounded annually. If you made a $69,000 deposit in each bank, how much more money would you earn from your second city bank account at the end of 10 years.

How much more: $13.168.49 First City Bank: $110,400 -Simple Interest: ($69,000*0.06=$4,140) $4,140*10 years= $41,400 $41,400+$69,000= $110,400 Second City Bank: $123,568.49 -N: 10 - PV: -$69,000 - I/Y: 6% -CPT FV: $123,568.49 Total: ($123,568.49-$110,400= $13,168.49)

You want to buy a new sports coupe for $76,500, and the finance office at the dealership has quoted you an APR of 5.8% for a 72 month loan to buy the car. what will your monthly payment be: what is the effective annual rate on this loan:

Monthly Payments: $1,260.62 -N:72 months -I/Y: 5.8%/12= 2.90 -PV:-$76,500 -CPT PMT: $1,260.62 EAR: 5.96% -NOM: 5.8% -C/Y: 12 -CPT EFF: 5.96%

You are ready to buy a house, and you have $30,000 for a down payment and closing costs. Closing costs are estimated to be 3.5% of the loan value. You have an annual salary of $48,000, and the bank is willing to allow your monthly mortgage payment to be equal to 28% of your monthly income. The interest rate on the loan is 9% per year with monthly compounding for a 30 year fixed rate loan: how much money will the bank loan you: how much can you offer for the house:

Monthly income: $48,000/12= $4,000 maximum payment: 0.28*$4,000= $1,120 N: 360 I/Y: 0.75% ( PMT: $1,120 CPT PV: $139,195.69 Total Price: Closing costs: .035*($139,195.69)= $4,871.85 Down Payment: $30,000-$4,871.85= $25,128.15 Total Price: $139,195.69+$25,128.15= $164,323.84

Good guys food established a trust fund that provides $125,000 in scholarships each year for needy students. The trust fund earns a fixed 7.25% rate of return. How much money did the firm contribute to the fund assuming that only the interest income is distributed?

PV: $125,000/0.0725=$1,724,138

The Maybe Pay life insurance Co. is trying to sell you an investment policy that will pay you and your heirs $26,000 per year forever. Suppose a sales associate told you the policy cost $471,000. At what interest rate would this be a fair deal?

Perpetuity problem: PV: C/r $471,000=$26,000/r r: $26,000/$471,000= .0552

You are ready to buy a house, and you have $20,000 for a down payment and closing costs. Closing costs are estimated to be 4% if the loan value. You have an annual salary of $36,000, and the bank is willing to allow your monthly mortgage to be equal to 28% if your monthly income. The interest rate on the loan is 6% per year with monthly compounding (0.5% per month) for a 30 year fixed loan:

Total cost: $154,500.80 -Monthly income: $36,000/12=$3,000.00 -Maximum payment: $3,000*0.28=$840.0 -30 years x 12 months: 360 N -30*12=360 -I/Y: 5% -PMT: -$840 -CPT PV: $140,104.96 Total price: -Closing costs: $140,104.96*0.04=$5,604.2 -Down payment: $20,000-$5,604.20=$14,395.8 -Total price: $140,105+$14,395.80=$154,500.8

Your broker calls you and tells you that he has this great investment opportunity. If you invest $100 today, you will receive $50 in one year and $80 in two. If you require 12% return on investment of this risk, should you take the investment? Also, how much are the cash flows worth today?

Year 1: $44.64 -FV: $50 -I/Y: 12% -N: 1 -CPT PV: $44.64 Year 2: $63.78 -FV: $80 -N: 2 -I/Y: 12% -CPT PV: $63.78 Total cash flow: $108.42 -$44.64+$63.78=$108.42

suppose a bond with a 10% coupon rate and semi annual coupons, has a face value of $1,000, 20 years to maturity and is selling for $1,197.93. is the YTM more or less than 10% what is the semi annual coupon payment how many periods are there

less 8% (4% * 2) 2

consider a bond with a 10% annual coupon rate, 15 years to maturity and a par value of $1,000. The current price is $928.09 will the yield be more or less than 10%

more than 10%

Suppose you are going to receive $14,000 per year for 6 years. The appropriate interest rate is 9.5% what is the present value if the payments are annuity due: suppose you plan to invest the payments for 6 years. what is the future value if the payments are ordinary annuity: what is the future value if the payments are annuity due:

what is the present value if the payment are annuity due: $63,645.49 -N: 6 -I/Y: 9.5% -PMT: $14,400 -CPT PV: $63,645.49 what is the PV if the payments are annuity due: $69,691.81 -N: 6 -I/Y: 9.5% -PMT: $14,400 -CPT PV: $69,691.81 what is the future value if the payments are ordinary annuity: $109,711.54 -N: 6 -I/Y: 9.5% -PMT:$14,400 -CPT FV: $109,711.54 What is the FV if the payments are annuity due: $129,134.14