Finance: Chapter 5 Review

Joseph Harris is considering an investment that pays 6.5 percent annually. How much must he invest today such that he will have $25,000 in seven years? (Round to the nearest dollar.)

$16,088

Joseph Ray just received an inheritance of $35,775 from his great aunt. He plans to invest the funds for retirement. If Joseph can earn 4.75% per year with quarterly compounding for 32 years, how much will he have accumulated? (Round off to the nearest dollar.)

$162,113 FV=PV*(1+i/m)^mn=35,775*(1+0.0475/4)^(4*32)=162,113.25

Dat Nguyen is depositing $17,500 in an account paying an annual interest rate of 8.25 percent compounded monthly. What is the interest on interest after six years?

$2,497.63 Deposit today = PV = $17,500 Interest rate = i = 8.25% No. of years = n = 6 Frequency of compounding = m = 2 Simple interest: Simple interest per year = $17,500 (0.0825) = $1,443.75 Simple interest for 6 years = $1,443.75 × 6 = $8,662.50 Future value with compound interest: = $17,500 × (1.006875)^72 = $28,660.13 Simple interest = $8,662.50 Interest on interest = $28,660.13 − $17,500 − $8,662.50 = $2,497.63

Tamera Watson is saving for her daughter's college education. She wants to have $50,000 available when her daughter graduates from high school in four years. If the investment she is considering will pay 8.25 percent compounded monthly, how much will she have to invest today to reach her target? (Round to the nearest dollar.)

$35,987 Return expected from investment = i = 8.25% Duration of investment = n = 4 years Frequency of compounding = m = 12 Target investment proceeds in 4 years = FV4 = $50,000 Present value of amount = PV FV=PV*(1+i/m)^mn=PV*(1+0.0825/12)^(12*4)=50000

If Norman invested $100,000 for 3 years at 12%, how much interest on interest will he earn? (Do not round intermediate calculations. Round the final answer to two decimal places.)

$4,492.80

Lorene Buckley wants to invest $3,500 today in a money market fund that pays a quarterly interest at 5 percent. She plans to fund a scholarship with the proceeds at her alma mater, Towson University. How much will Lorene have at the end of seven years? (Round to the nearest dollar.)

$4,956 Amount invested today = PV = $3,500 Interest rate on money market account = i = 5% Duration of investment = n = 7 years Frequency of compounding = m = 4 Value of investment after 7 years = FV7 FV7 = PV × (1 + i/m)m×n = $3,500 × (1 + 0.05 / 4)4×7 = $3,500 × (1.0125)28 = $4,955.97

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? (Round to the nearest dollar.)

$44,059

Leroy Diaz plans to invest some money today so that he will receive $7,500 in three years. If the investment he is considering will pay 3.65 percent compounded daily, how much will he have to invest today?

$6,722

Camille Noah is investing $5,000 in an account paying 6.75 percent annually for three years. What is the interest on interest if interest is compounded?

$69.88 Deposit today = PV = $5,000 Interest rate = i = 6.75% No. of years = n = 3 Simple interest: Simple interest per year = $5,000 × (0.0675) = $337.50 Simple interest for 3 years = $337.50 × 3 = $1,012.50 Future value with compound interest: FV3 = $5,000 (1 + 0.0675)3 = $6,082.38 Simple interest = $1,012.50 Interest on interest = $6,082.38 - $5,000 - $1,012.50 = $69.88

Jack Palomo has deposited $2,500 today in an account paying 6 percent interest annually. What would be the simple interest earned on this investment in five years? If the account paid compound interest, what would be the interest on interest in five years?

$750; $95.56 Deposit today = PV = $2,500 Interest rate = i = 6% No. of years = n = 5 Simple interest: Simple interest per year = $2,500 × (0.06) = $150.00 Simple interest for 5 years = $150 × 5 = $750.00 Future value with compound interest: FV5 = $2,500 (1 + 0.06)5 = $3,345.56 Simple interest = $750 Interest on interest = $3,345.56 − $2,500 − $750 = $95.56

Patrick Smith has $5,000 to invest in a small business venture. His partner has promised to pay him back $8,200 in five years. What is the return earned on this investment?

10.4% Amount being invested = PV = $5,000 Amount to be paid back after 5 years = FV = $8,200 Interest rate on investment = i = ? Duration of investment = n = 5 years Present value of investment = PV

If you can invest $200,000 at a 10.5% annual rate, compounded monthly, how long will it take to have $500,000? (Do not your intermediate calculations. Round your final answer to the nearest whole month.)

105 months

Boretti has $400,000 in a stock fund. The fund pays a 10% return, compounded annually. If he does not make another deposit into the account, how long will it take for the account to increase to $2 million? (Do not round intermediate calculations. Round the final answer to two decimal places.)

16.89 years

Your mother is trying to choose one of the following bank CDs to deposit $10,000. Which will have the highest future value if she plans to invest for three years? a. 3.40% compounded quarterly b. 3.50% compounded daily c. 3.25% compounded monthly d. 3.75% compounded annually

3.75% compounded annually A) Interest rate on CD = i = 3.50% Frequency of compounding = m = 365 Value of investment after 3 years = FV3 FV3 = PV × (1 + i/m)m×n = $10,000 × (1 + 0.035/365)365×3 = $10,000 × (1.00009589)1,095 = $11,107.05 B) Interest rate on CD = i = 3.25% Frequency of compounding = m = 12 Value of investment after 3 years = FV3 FV3 = PV × (1 + i/m)m×n = $10,000 × (1 + 0.0325/12)12×3 = $10,000 × (1.0027908333)36 = $11,022.66 C) Interest rate on CD = i = 3.40% Frequency of compounding = m = 4 Value of investment after 3 years = FV3 FV3 = PV × (1 + i/m)m×n = $10,000 × (1 + 0.034/4)4×3 = $10,000 × (1.0085)12 = $11,069.06 D) Interest rate on CD = i = 3.75% Frequency of compounding = m = 1 Value of investment after 3 years = FV3 FV3 = PV × (1 + i/m)m×n = $10,000 × (1 + 0.0375) = $10,000 × (1.0375)3 = $11,167.71

Your tuition for the coming year is due today. You borrow $8,000 from your uncle and agree to repay in the three years an amount of $9,250. What is the interest rate on this loan? Round to the nearest percent.

5% Amount to be borrowed = PV = $8,000 Amount to be paid back after 3 years = FV3 = $9,250 Interest rate on investment = i = ? Duration of investment = n = 3 years Present value of investment = PV