Exam 2: Homework #3 Flashcards
(24 cards)
Which of the following investments will have the highest future value?
a. $1,300 invested at an annual interest rate of 10% for 5 years
b. $1,000 invested at a quarterly interest rate of 2.25% for 10 years
c. $1,300 invested at a quarterly interest rate of 2.25% for 5 years
d. $1,000 invested at an annual interest rate of 10% for 10 years
A: $1000 invested at an annual interest rate of 10% for 10 years
1,300(1.1)^5 = $2,093.66
1,000(1.0225)^40 = $2,435.19
1,300(1.0225)^20 = $2,028.66
1,000(1.1)^10 = $2,593.74
You are interested in investing $15,000, a gift from your grandparents, for the next four years in a mutual fund that will earn an annual return of 8 percent. What will your investment be worth at the end of four years?
A: $20,407
Present value of the investment = PV = $15,000
Return on mutual fund = i = 8%
No. of years = n = 4
FV4 = PV x (1+i)^n = $15,000 x (1.08)^4 = $20,407.33
Financial calculator solution: PV = -$15,000; N = 4; I/Y = 8; PMT = 0; CPT FV = $20,407.33
What is the future value of $1,500 after 5 years if the annual return is 6%, compounded semiannually?
A: $2,016
Present value of the investment = PV = $1,500
Return = i = 6%/2 = 3%
No. of years times periods per year = n = 5 x 2 = 10
FV10 = PV x (1 + i)^n = $1,500 x (1.03)^10 = $2,015.87
Financial calculator solution: PV = -1,500; N = 10; I/Y = 3; PMT = 0; CPT FV = $2,015.87
Your bank pays 5 percent annual interest compounded semiannually on your savings account. You don’t expect to add to the current balance of $2,700 over the next four years. How much money can you expect to have at the end of this period? (Round intermediate calculations to 6 decimal places, e.g. 2.412512 and final answer to 2 decimal places, e.g. 2,515.25.)
A: 3,289.68
Amount invested today = PV = $2,700
Return expected from investment = i = 5%
Duration of investment = n = 4 years
Frequency of compounding = m = 2
Value of investment after 4 years = FV4
FV4 = PV x (1+ i/m)^mxn = 2,700 x (1 +o.o5/2)^2x4
FV4 = $2,700 x (1.025)^8 = $3,289.69
Maria Addai has been offered a future payment of $750 two years from now. If she can earn an annual rate of 6.5 percent, compounded daily, on her investment, what should she pay for this investment today? (Round intermediate calculations to 6 decimal plaes, e.g. 1.23523 and final answer to 2 decimal places, e.g., 400.56)
Value of investment after 2 years = FV2 = $750
Return expected from investment = i = 6.5%
Duration of investment = n = 2 years
Compounding frequency per year = 365
Amount to be invested today = PV
PV = FVn / (1+i/m)^nxm = $750 / (1.00018)^730 = $658.62
Elizabeth Sweeney wants to accumulate $12,000 by the end of 12 years. If the annual interest rate is 7.0 percent and interest compounds semiannually, how much will she have to invest today to achieve her goal? (Round intermediate calculations to 6 decimal places, e.g. 2.512512 and final answer to 2 decimal places, e.g. 2,515.25)
A: $5,255.49
Amount Ms. Sweeney wants at the end of 12 years = FV12 = $12,000
Interest rate on investment = i = 7.0%
Duration of investment = n = 12 years
Compounding frequency per year = 365
Present value of investment = PV
PV = FVn / (1 + i/m)^nxm = $12,000 /
(1.0350)^24 = $5,255.49
A preferred stock would be an example of:
a. a perpetuity
b. an ordinary annuity
c. an annuity due
d. a growing annuity
a. a perpetuity
Stuart Weddie’s father is 55 years old and wants to set up a cash flow stream that would be forever. He would like to receive $15,000 every year, beginning at the end of this year. These payments would then continue to future generations indefintely. If he could invest in an account earning 9 percent annually, how much would he have to invest today to receive his perpetual cash flow?
A: $166,667
Annual payment needed = PMT = $15,000
Investment rate of return = i = 9%
Term of payment = Perpetuity
Present value of investment needed = PV
PV of Perpetuity = PMT / i
= $15,000 / 0.09
= $166,666.67
Nick invested $2,000 in a bank savings account today and another $2000 a year from now. If the bank pays interest of 10 percent per year, how much money will Nick have at the end of two years?
A: $4,620
Future value of two cash flows = [PV x (1+i)^2] +[PV x (1+i)]
= [$2000 x (1+0.10)^2] +[$2000 x (1+0.10)]
=[$2000 x (1.10)^2] +[$2000 x (1.10)]
= [$2000 x 1.21^2] +[$2000 x 1.10]
= $2,420 + $2,200
= $4,620
A lottery winner was given a perpetual payment of $25,362. She could invest the cash flows at 7.5 percent annually. What is the present value of this perpetuity?
A: $338,160
Annual payment needed = PMT = $25,362
Investment rate of return = i = 7.5%
Term of payment = Perpetuity
Present value of investment needed = PV
PV of Perpetuity = PMT / i
= $25,362 / 0.075
= $338,160
Brandon Ramirez wants to set up a scholarship at his alma mater. He is willing to invest $320,000 in an account earning 11 percent annually. What will be the annual scholarship that can be given from this investment?
A: $35,200
Annual payment needed = PMT
Present value of investment = PVA = $320,000
Investment rate of return = i = 11%
Term of payment = Perpetuity
PV of Perpetuity = PMT / i
PMT = PV of Perpetuity x i
= $320,000 x 0.11
= $35,200
Sid Phillips has funded a retirement investment with $250,000 earning a return of 6.75 percent annually. what is the value of the payment that he can receive in perpetuity?
A: $16,875
Annual payment needed = PMT
Present value of investment = PVA = $250,000
Investment rate of return = i = 6.75%
Term of payment = Perpetuity
PV of Perpetuity = PMT / i
PMT = PV of Perpetuity x i
= $250,000 x 0.0675
= $16,875
Ralf Wilson wants to receive $25,000 in perpetuity and will invest his money in an investment that will earn a return of 14 percent annually. What is the value of the investment that he needs to make today to receive his perpetual cash flow stream?
A: $178,571
Annual Payment needed = PMT = $25,000
Investment rate of return = i = 14%
Term of payment = Perpetuity
Present value of investment needed = PV
PV of Perpetuity = PMT / i
= $25,000/0.14
= $178,571.43
Joeseph Ray just received an inheritance of $35,775 from his great aunt. He plans to invest the funds for retirement. If Joseph can ean 4.75% per year with quarterly compounding for 32 years, how much will he have accumulated?
A: $162,113
Amount invested today = PV = $35,775
Frequency of compounding = m = 4
Interest rate = i = 4.75% / 4 = 1.1875%
Duration of investment = n = 32 years x 4 = 128 periods
Value of investment after 7 years, or 128 periods = FV128 = $162,113.25
FV32 = PV x (1 +i/m)^mn = $35,775 x (1 +0.0475/4)^4x32
= $35,775 x (1.011875)^128
= $35,775 x 4.531467
= $162,113.25
Your aunt is looking to invest a certain amount today. Which of the following choices will give the maximum interest?
a. Three-year CD at 6.5% annual rate
b. Three-year CD at 6.75% annual rate
c. Three-year CD at 6.26% annual rate
d. Three-year CD at 7% annual rate
d. Three-year CD at 7% annual rate
Juan Vinson is planning to buy a house in five years. He is looking to invest $25,000 today in an index mutual fund that will provide him a return of 12 percent annually. How much will he have at the end of five years?
A: $44,059
Present value of the investment = PV = $25,000
Return on mutual fund = i = 12%
No. of years = n = 5
FV5 = PV x (1+i)^n = $25,000 x (1.12)^5
= $44,058.54
Financial calculator solution: PV = -$25,000; N=5; I/Y = 12; PMT = 0; CPT FV = $44,058.54
Carlos Lopes is looking to invest for the next three years. He is looking to invest $7,500 today in a bank CD that will earn interest at 5.75 percent annually. How much will he have at the end of three years?
A: $8,870
Present value of the investment = PV = $7,500
Interest rate on CD - i = 5.75%
No. of years = n = 3
FV3 = PV x (1+i)^n = $7,500 x (1.0575)^3 = $8,869.57
Financial Calculator solution: PV = -$7,500; PMT = 0; I/Y = 5.75; N = 3; CPT FV = $8,869.57
Joseph Harris is considering an investment that pays 6.5 percent annually. How much does he need to invest today so that he will have $25,000 in seven years? (Round to the nearest dollar)
A: $16,088
Value of investment after 7 years = FV7 = $25,000
Return expected from investment = i = 6.5%
Duration of investment = n = 7 years
Amount to be invested todya =PV
PV = FVn / (1+i)^n = $25,000 / (1.065)^7 = $16,087.66
Financial calculator solution: FV = 25,000; N = 7; I/Y = 6.5; PMT = 0; CPT = $16,087.66
Juan and Rachel Burpo plan to buy a time-share in six years of $16,860. In order to have adequate funds to do so, the Burpo want to make a deposit to their money market fund today. Assume that they will be able to earn an investment rate of 5.75%, compounded annually. How much will Juan and Rachel need to deposit today to achieve their goal?
A: $12,055
Amount needed = FV = $16,860
Interest rate = i = 5.75%
Duration of investment = n = 6 years
Present Value = PV6 = $12,055.22
PV6 = FV / (1+i)^n = $16,860 / (1.0575)^6
= $16,860 / 1.398564
= $12,055.22
Financial calculator solution: FV = 16,860; N=6; I/Y = 5.75; PMT = 0; CPT PV = $12,055.22
Steve Fisher is saving for a new car. He needs to have $21,000 for the car in three years. How much will he have to invest today in an account paying 8 percent annually to achieve his target?
A: $16,670
Value of investment after 3 years = FV3 = $21,000
Return expected from investment = i = 8%
Duration of investment = n = 3 years
Amount to be invested today = PV
PV = FVn / (1+i)^n = $21,000/(1.08)^3 = $16,670.48
Financial calculator solution: FV = 21,000; N = 3; I/Y = 8; PMT = 0; CPT PV = $16,670.48
Albert borrows money from Jacob today with a promise to repay $7,418.87 in four years. If Jacob could earn 5.45 percent annually on the any investment he makes today, how much would he be willing to lend Albert today?
A: $6,000
Loan repayment amount after 4 years = FV4 = $7,418.87
Return expected from loan = i = 5.45%
Duration of loan = n = 4 years
Amount to be loaned today= PV
PV = FVn / (1+i)^n = $7,418.87 / (1.p545)^4 = $6,000
Financial calculator solution: FV = 7,418.87; N = 4; I/Y = 5.45; PMT = 0; CPT PV = $6,000
Joyce Thomas wants to buy a house in six years. She hopes to have $25,000 at that time. If the bank CD she wants to invest in will pay 7.5 percent annually, how much will she have to invest today?
A: $16,199
Amount needed for down payment after 6 years = FV6 = $25,000
Return expected from investment = i = 7.5%
Duration of investment = n = 6 years
Amount to be invested today = PV
PV = FVn / (1+i)^n = $25,000 / (1.075)^6 = $16,199
Financial calculator solution: FV = 25,000; N = 6; I/Y = 7.5; PMT = 0; CPT PV = $16,199.04
Robert Kelly wants to start a business in 10 years. He hopes to have $100,000 at that time to invest in the business. To reach his goal, he plans to invest a certain amount today in a bank CD that will pay him 9.50 percent annually. How much will he have to invest today to achieve his target?
A: $40,351
Value of investment after 10 years = FV10 = $100,000
Return expected from investment = i = 9.5%
Duration of investment = n = 10 years
Amount to be invested today = PV
PV = FVn / (1+i)^n = $100,000 / (1.095)^10 = $40,351.42
Financial calculator solution: FV = 100,000; N = 10; I/Y = 9.5; PMT = 0; CPT PV = $40,351.42
You need to have $15,000 in five years to pay off a home equity loan. You can invest in an account that pay 5.75 percent compounded quarterly. How much will have to invest today to attain your target in five years?
A: $11,275
Return expected from investment = i = 5.75%
Duration of investment = n = 5 years
Frequency of compounding = m = 4
Target investment proceeds in 5 years = FV5 = $15,000
Present Value of amount = PV
PV = FVn / [1+i/m]^mn = $15,000 / [1 + 0.0575/4]^5x4 = $15,000 / (1.014375)^20
= $11,275.10
Financial calculator solution: FV = 15,000; N = 20; I/Y = 5.75/4; PMT = 0; CPT PV = $11,275.10
