Chapter 5 Homework
d. What is the present value of a $60 perpetuity discounted back to the present at 11 percent?
60/.11 =545.45
a. What is the present value of a $650 perpetuity discounted back to the present at 14 percent?
650/.14 =4,642.68
b. What is the present value of a $1,500 perpetuity discounted back to the present at 18 percent?
1,500/.18 =8,333.33
c. What is the present value of a $110 perpetuity discounted back to the present at 15 percent?
110/.15 =733.33
(Complex present value) You would like to have $56,000 in 14 years. To accumulate this amount you plan to deposit each year an equal sum in thebank, which will earn 6 percent interest compounded annually. Your first payment will be made at the end of the year. a. How much must you deposit annually to accumulate $56,000 in 14 years?
FV= $56,000 Annual rate= 6% Periods= 14 Payments= 2,664.75
b. If you decide to make a large lump-sum deposit today instead of the annual deposits, how large should this lump-sum deposit be? (Assume you can earn 6 percent on this deposit.)
FV= $56,000 Annual rate= 6% Periods= 14 Payments= 0 PV= $24,768.85
(Present value) The Kumar Corporation is planning on issuing bonds that pay no interest but can be converted into $2,000 at maturity, 19 years from their purchase. To price these bonds competitively with other bonds of equalrisk, it is determined that they should yield 12 percent, compounded annually. At what price should the Kumar Corporation sell thesebonds?
Kumar Corporation should sell these bonds at $232.21
(Future value of an annuity) In 11 years you are planning on retiring and buying a house inOviedo, Florida. The house you are looking at currently costs $160,000 and is expected to increase in value each year at a rate of 3 percent. Assuming you can earn 14 percent annually on yourinvestments, how much must you invest at the end of each of the next 11 years to be able to buy your dream home when youretire? a. If the house you are looking at currently costs $160,000 and is expected to increase in value each year at a rate of 3 percent, what will the value of the house be when you retire in 11 years?
PV= $160,000 Payments= 0 Annual rate= 3% Periods= 11 **Annually FV=$221,477.42
d. To what amount will $20,000 invested for 4 years at 6 percent compounded annually accumulate?
PV= $20,000 Payment= 0 Annual rate= 6% Periods= 4 Annually FV= $25,249.54
(Compound value solving for r) At what annual rate would the following have to be invested? a. $490 to grow to $1,057.87 in 10 years b. $320 to grow to $507.80 in 6 years c. $50 to grow to $509.87 in 19 years d. $200 to grow to $243.10 in 4 years a. At what annual rate would $490 have to be invested to grow to $1,057.87 in 10 years?
PV= $490 Payment= 0 FV= $1,057.87 Periods= 10 Annual rate=
b. To what amount will $7,800 invested for 7 years at 7 percent compounded annually accumulate?
PV= $7,800 Payment= 0 Annual rate= 7% Periods= 7 Annually FV= $12,525.10
c. To what amount will $795 invested for 11 years at 12 percent compounded annually accumulate?
PV= $795 Payment= 0 Annual rate= 12% Periods= 11 Annually FV= $2,765.45
a. If the house you are looking at currently costs $110,000 and is expected to increase in value each year at a rate of 3 percent, what will the value of the house be when you retire in 6 years?
PV= -110,000 Payments= 0 Annual rate= 3% Periods= 6 FV= 131,345.75
At what annual rate would $204 have to be invested to grow to $247.96 in 4 years?
PV= -204 Payments= 0 FV= 247.96 Periods= 4 Annual rate= 5%
At what annual rate would $290 have to be to invested to grow to $536.79 in 8 years?
PV= -290 Payments= 0 FV= 536.79 Periods= 8 Annual rate= 8%
(Solving for n) Jack asked Jill to marryhim, and she has accepted under onecondition: Jack must buy her a new $350,000 Rolls-Royce Phantom. Jack currently has $44,200 that he may invest. He has found a mutual fund with an expected annual return of 4.2% in which he will place the money. How long will it take Jack to winJill's hand inmarriage? Ignore taxes.
PV= -44,200 Payments= 0 FV= 350,000 Rate= 4.2% Periods= 50.29
At what annual rate would $50 have to be invested to grow to $602.78 in 19 years?
PV= -50 Payments= 0 FV= 602.78 Periods= 19 Annual rate= 14%
At what annual rate would $510 have to be invested to grow to $1,148.62 in 12 years?
PV= -510 Payments= 0 FV= 1,148.62 Periods= 12 Annual rate= 7%
b. What is the future sum of $6,000 in a bank account for 6 years at an APR of 5 percent compounded semiannually?
PV= -6,000 Payments= 0 Annual rate= 2.5% Periods= 12 FV= 8,069.33 ANNUALLY
a. What is the future sum of $6,000 in a bank account for 6 years at an APR of 5 percent?
PV= -6,000 Payments= 0 Annual rate= 5% Periods= 6 FV= 8,040.57
b. Assuming you can earn 8 percent annually on your investments, how much must you invest at the end of each of the next 6 years to be able to buy your dream home when you retire?
PV= 0 FV= 131,345.75 Annual rate= 8% Periods= 6 Payments= 17,904.45
Judge whether the following statement about the shape of the sales trend line is true or false.
"The sales trend graph is not linear, because this is a compound growth trend." True
(Compound annuity) You plan on buying some property in Florida 7years from today. To do this you estimate that you will need $40,000 at that time for the purchase. You would like to accumulate these funds by making equal annual deposits in your savings account, which pays 12 percent annually. If you make your first deposit at the end of this year, and you would like your account to reach $40,000 when the final deposit is made, what will be the amount of your deposits?
PV= 0 FV= 40,000 Annual rate= 12% Periods= 7 Payments= 3,964.71
b. What is the accumulated sum of $100 a year for 8 years compounded annually at 8 percent?
PV= 0 Payments= 100 Annual rate= 8% Periods= 8 FV= $1,063.66
d. What is the accumulated sum of $24 a year for 6 years compounded annually at 5 percent?
PV= 0 Payments= 24 Annual rate= 5% Periods= 6 FV= $163.25
c. What is the accumulated sum of $35 a year for 12 years compounded annually at 11 percent?
PV= 0 Payments= 35 Annual rate= 11% Periods= 12 FV= $794.96
(Compound annuity) What is the accumulated sum of each of the following streams of payments? a. $490 a year for 9 years compounded annually at 9 percent. b. $100 a year for 8 years compounded annually at 8 percent. c. $35 a year for 12 years compounded annually at 11percent. d. $24 a year for 6 years compounded annually at 5 percent. a. What is the accumulated sum of $490 a year for 9 years compounded annually at 9 percent?
PV= 0 Payments= 490 Annual rate= 9% Periods= 9 FV= $6,380.31
What is the accrued value of $10,000 in a savings account paying annual compound interest of 6 percent for 16 years?
PV= 10,000 Payments= 0 Annual rate= 6% Periods= 16 FV= $25,403.52
d. What is the present value of $1,200 to be received 5 years from now discounted back to the present at 18 percent?
Payments= 0 FV= $1,200 Annual rate= 18% Period= 5 PV= $524.53
b. What is the present value of $200 to be received 6 years from now discounted back to the present at 8 percent?
Payments= 0 FV= $200 Annual rate= 8% Periods= 6 PV= $126.03
What is the current balance in Nick's retirement fund?
$376,499.73+$140,637.02 =$517,136.75
a. What is the present value of investment A at 18 percent annual discount rate?
Payments= -17,000 Annual rate= 18% Periods= 5 PV= 53,161.91
e. With respect to the effect of changes in the stated interest rate and holding periods on future sums, which of the following statements is correct? (Select the best choice below.)
D. An increase in the stated interest rate will increase the future value of a given sum. Likewise, an increase in the length of the holding period will increase the future value of a given sum.
c. What is the present value of $1,150 to be received 11 years from now discounted back to the present at 4 percent?
Payments= 0 FV= $1,150 Annual rate= 4% Periods= 11 PV= $747.02
(Solving for r of an annuity) You lend a friend $40,000, which your friend will repay in 10 equal annualend-of-year payments of $7,000, with the first payment to be received 1 year from now. What rate of return does your loanreceive?
PV = -$40,000 Payments = 7,000 FV = 0 Periods = 10 Annual rate = 11.73%
(Solving for r in compound interest) You lend a friend $9,000, for which your friend will repay you $14,000 at the end of 7 years. What interest rate are you charging yourfriend?
PV = -9,000 Payments = 0 FV = 14,000 Periods = 7 Annual rate = 6.52%
(Compound value) Stanford Simmons, who recently sold his Porsche, placed $10,000 in a savings account paying annual compound interest of 6 percent. a. Calculate the amount of money that will have accrued if he leaves the money in the bank for 3, 6, and 16 years. b. If he moves his money into an account that pays 8 percent or one that pays 10 percent, rework part (a) using these new interest rates. c. What conclusions can you draw about the relationship between interest rates, time, and future sums from the calculations you have completed in this problem? a. What is the accrued value of $10,000 in a savings account paying annual compound interest of 6 percent for 3 years?
PV= 10,000 Payments= 0 Annual rate= 6% Periods= 3 FV= $11,910.16
What is the accrued value of $10,000 in a savings account paying annual compound interest of 6 percent for 6 years?
PV= 10,000 Payments= 0 Annual rate= 6% Periods= 6 FV= $14,185.19
b. If the money was moved to an account that pays 8 percent, what is the accrued value of $10,000 in the account for 3 years?
PV= 10,000 Payments= 0 Annual rate= 8% Periods= 3 FV= $12,597.12
(Future value) Sales of a new finance book were 12,000 copies this year and were expected to increase by 23 percent per year. What are expected sales during each of the next 3 years? Graph this sales trend and explain. a. If the 12,000 copies of book sales this year were expected to increase by 23 percent per year, what are the expected sales of the new finance book next year?
PV= 12,000 Payments= 0 Annual rate= 23% Periods= 1 FV= 14,760
b. If the 12,000 copies of book sales this year were expected to increase by 23 percent per year, what are the expected sales of the new finance book in two years?
PV= 12,000 Payments= 0 Annual rate= 23% Periods= 2 FV= 18,154.8
c. If the 12,000 copies of book sales this year were expected to increase by 23 percent per year, what are the expected sales of the new finance book in three years?
PV= 12,000 Payments= 0 Annual rate= 23% Periods= 3 FV= 22,330.4
(Compound interest) To what amount will the following investments accumulate? a. $5,000 invested for 10 years at 10 percent compounded annually. b. $7,800 invested for 7 years at 7 percent compounded annually. c. $795 invested for 11 years at 12 percent compounded annually. d. $20,000 invested for 4 years at 6 percent compounded annually. a. To what amount will $5,000 invested for 10 years at 10 percent compounded annually accumulate?
PV= 5,000 Payment= 0 Annual rate= 10% Periods= 10 Annually FV= $12,968.71
a. Giancarlo Stanton hit 50 home runs in 2014. If his home-run output grew at a rate of 11 percent per year, what would it have been in 2015?
PV= 50 Payment= 0 Annual rate= 11% Periods= 1 FV= 55.5
b. Giancarlo Stanton hit 50 home runs in 2014. If his home-run output grew at a rate of 11 percent per year, what would it have been in 2016?
PV= 50 Payment= 0 Annual rate= 11% Periods= 2 FV= 61.61
c. Giancarlo Stanton hit 50 home runs in 2014. If his home-run output grew at a rate of 11 percent per year, what would it have been in 2017?
PV= 50 Payment= 0 Annual rate= 11% Periods= 3 FV= 68.38
d. Giancarlo Stanton hit 50 home runs in 2014. If his home-run output grew at a rate of 11 percent per year, what would it have been in 2018?
PV= 50 Payment= 0 Annual rate= 11% Periods= 4 FV= 75.9
e. Giancarlo Stanton hit 50 home runs in 2014. If his home-run output grew at a rate of 11 percent per year, what would it have been in 2019?
PV= 50 Payment= 0 Annual rate= 11% Periods= 5 FV= 84.25
If the money was moved to an account that pays 10 percent, what is the accrued value of $10,000 in the account for 16 years?
PV=10,000 Payments= 0 Annual rate= 10% Periods= 16 FV= $45,949.73
If the money was moved to an account that pays 10 percent, what is the accrued value of $10,000 in the account for 3 years?
PV=10,000 Payments= 0 Annual rate= 10% Periods= 3 FV= $13,310.00
If the money was moved to an account that pays 10 percent, what is the accrued value of $10,000 in the account for 6 years?
PV=10,000 Payments= 0 Annual rate= 10% Periods= 6 FV= $17,715.61
If the money was moved to an account that pays 8 percent, what is the accrued value of $10,000 in the account for 16 years?
PV=10,000 Payments= 0 Annual rate= 8% Periods= 16 FV= $34,259.43
If the money was moved to an account that pays 8 percent, what is the accrued value of $10,000 in the account for 6 years?
PV=10,000 Payments= 0 Annual rate= 8% Periods= 6 FV= $15,868.74
(Present value of an uneven stream of payments) You are given three investment alternatives to analyze. The cash flows from these three investments are shown in the popup window: LOADING.... Assuming a discount rate of 17 percent, find the present value of each investment. a. What is the present value of investment A at 17 percent annual discount rate?
Payments= -14,000 Annual rate= 17% Periods= 5 PV= $44,790.85
b. If 16 percent is the appropriate discount rate, what is the present value of the cash flows?
Payments= -150,000 FV= 0 Annual rate= 16% Periods= 20 PV= 889,326.13 PV*1.16 PV= 1,031,618.31
(Present value) The statelottery's million-dollar payout provides for $3 million(s) to be paid over 19 years in 20 payments of $150,000. The first $150,000 payment is madeimmediately, and the 19 remaining $150,000 payments occur at the end of each of the next 19 years. If 8 percent is the appropriate discountrate, what is the present value of this stream of cashflows? If 16 percent is the appropriate discountrate, what is the present value of the cashflows? a. If 8 percent is the appropriate discount rate, what is the present value of this stream of cash flows?
Payments= -150,000 FV= 0 Annual rate= 8% Periods= 20 PV= 1,472,722.11 PV*1.08 PV=1,590,539.88
(Present value) What is the present value of the following future amounts? a. $900 to be received 10 years from now discounted back to the present at 10 percent. b. $200 to be received 6 years from now discounted back to the present at 8 percent. c. $1,150 to be received 11 years from now discounted back to the present at 4 percent. d. $1,200 to be received 5 years from now discounted back to the present at 18 percent. a. What is the present value of $900 to be received 10 years from now discounted back to the present at 10 percent?
Payments= 0 FV= $900 Annual rate= 10% Periods= 10 PV= $346.99
(Solving for r in an annuity) Your folks just called and would like some advice from you. An insurance agent just called them and offered them the opportunity to purchase an annuity for $9,236.33 that will pay them $1,500 per year for 15 years, but theydon't have the slightest idea what return they will be making on their investment of $9,236.33. What rate of return will they beearning? The annual rate of return they will be earning is...?
Payments= 1,500 FV= 0 PV= -9,236.33 Periods= 15 R= 13.95%
b. Nick received an inheritance check for $30,000 from his beloved uncle 20 years ago and deposited the entire amount into his retirement fund earning 7.8% interest compounded quarterly. How much has this amount accumulated in the retirement account?
Periods= 20x4=80 Annual rate= 7.8%/4=1.95 Payments=0 PV= 30,000 ANNUALlY **FV=$140,637.02
(Nonannual compounding using a calculator) Jesse Pinkman is thinking about trading cars. He estimates he will still have to borrow $22,000 to pay for his new car. How large willJesse's monthly car loan payment be if he can get a 3-year (36 equal monthlypayments) car loan from the university's credit union at an APR of 7.2 percent compoundedmonthly?
Periods= 36 Annual rate= 7.2%/12=.6 PV=22,000 FV=0 Annually Payments= $681.31
c. At the end of 5 years you will receive $8,000 and deposit this in the bank toward your goal of $42,000 at the end of 10 years. In addition to this deposit, how much must you deposit in equal annual deposits to reach your goal? (Again assume you can earn 8 percent on this deposit.)
STEP 1. PV= 8,000 Annual rate= 8% Periods= 5 FV= 11,754.62 42,000-11,754.62=30,245.38 STEP2. FV=30,245.38 Annual rate= 8% Periods= 10 Payments= $2,087.82
c. What is the present value of investment C at 16 percent annual discount rate? (Year 1= $17,000 Year 2= $85,000 Year 3= $17,000)
STEP 1. TVM CALC. FV= 17,000 Annual rate= 16% Periods= 1 PV= $14,655.17 Compounded annually STEP 2. FV= 85,000 Annual rate= 16% Periods= 6 PV= $34,887.59 STEP 3. FV= 17,000 Annual rate= 16% Periods= 10 PV= $3,853.62 STEP 4. $14,655.17+$34,887.59+$3,853.62 =$53,396.38
b. What is the present value of investment B at 16 percent annual discount rate? ($17,000 for 6 years)
STEP 1. TVM CALC. Payments= 17,000 Annual rate= 16% Periods= 6 PV=62,640.51 Compounded annually STEP 2. Payments= 0 Annual rate= 16% Periods= 4 FV=62,640.51 PV= $34,595.80
(Complex annuity) Upon graduating from college 40 years ago, Dr. Nick Riviera was already thinking of retirement. Since then he has made deposits into his retirement fund on a quarterly basis in the amount of $350. Nick has just completed his final payment and is at last ready to retire. His retirement fund has earned 7.8% interest compounded quarterly. a. Since graduating from college 40 years ago, Dr. Nick Riviera has made deposits into his retirement fund on a quarterly basis in the amount of $350. If his retirement fund has earned 7.8% interest compounded quarterly, how much has Nick accumulated in his retirement account?
TVM CALC Annual rate= 7.8%/4=1.95 Payment= -350 Periods=40x4=160 PV=0 ANNUALLY **FV= $376,499.73
b. If you decide to make a large lump-sum deposit today instead of the annual deposits, how large should this lump-sum deposit be? (Assume you can earn 8 percent on this deposit.)
TVM CALC FV= $42,000 Annual rate= 8% Periods= 10 Compounded annually FV= $19,454.13
(Complex present value) You would like to have $42,000 in 10 years. To accumulate this amount you plan to deposit each year an equal sum in thebank, which will earn 8 percent interest compounded annually. Your first payment will be made at the end of the year. a. How much must you deposit annually to accumulate $42,000 in 10 years?
TVM CALC FV= $42,000 Annual rate= 8% Periods= 10 Compounded annually Payments=$2,899.24
a. What is the present value of investment A at 16 percent annual discount rate? ($17,000 for 5 years)
TVM CALC. Payments= -17,000 Annual rate= 16% Periods= 5 Compounded annually PV= $55,662.99
(Compound interest with nonannual periods) b. What is the future sum of $6,000 in a bank account for 8 years at an APR of 4 percent compounded semiannually?
TVM CALC. Present value= $6000 Payments= 0 Annual rate= 2% Periods= 16 Compounded annually FV= $8,236.71
d. What is the future sum of $6,000 in a bank account for 16 years at an APR of 4 percent?
TVM CALC. Present value= $6000 Payments= 0 Annual rate= 4% Periods= 16 Compounded annually FV= $11,237.89
(Compound interest with nonannual periods) a. What is the future sum of $6,000 in a bank account for 8 years at an APR of 4 percent?
TVM CALC. Present value= $6000 Payments= 0 Annual rate= 4% Periods= 8 Compounded annually FV= $8,211.41
What is the future sum of $6,000 in a bank account for 8 years at an APR of 4 percent compounded bimonthly (every two months)?
TVM CALC. Present value= $6000 Payments= 0 Annual rate= 4%/6 =.66666666667 or 2/3 Periods= 8*6=48 Compounded annually FV= $8,254
c. What is the future sum of $6,000 in a bank account for 8 years at an APR of 8 percent?
TVM CALC. Present value= $6000 Payments= 0 Annual rate= 8% Periods= 8 Compounded annually FV= $11,105.58
What is the future sum of $6,000 in a bank account for 8 years at an APR of 8 percent compounded bimonthly (every two months)?
TVM CALC. Present value= $6000 Payments= 0 Annual rate= 8%/6 =1.333333333 Periods= 8*6 =48 Compounded annually FV= $11,330.86
What is the future sum of $6,000 in a bank account for 8 years at an APR of 8 percent compounded semiannually?
TVM CALC. Present value= $6000 Payments= 0 Annual rate= 8/2=4% Periods= 8*2=16 Compounded annually FV= $11,237.89
c. What conclusions can you draw about the relationship between interest rates, time, and future sums from the calculations you have completed in this problem?
There is a positive relationship between both the interest rate used to compound a present sum and the number of years for which the compounding continues and the future value of that sum.
