Finance Chapter 5

Which of the following investments will have the highest future value?

$1,000 invested at an annual interest rate of 10% for 10 years

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 that this investment earns?

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 PV = FV(n)/ (1+i)^n 5,000 = 8200/(1+ i)^5 (1+i)^5 = 8200/5000 = 1.64 (1+i) = (1.64)^1/5 = 1.103999 i= 10.4%

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?

3.75% compounded annually 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

Which of the following situations will result in an increase in the future value of an investment?

An increase in the rate of interest

Money has time value because:

people can earn interest on money that is invested

Future value measures:

what one or more cash flows are worth at the end of a specified period

The time value of money concept recognizes that people require additional compensation for deferring consumption.

True

Which of the following statements about the time value of money is true?

The further in the future you receive a dollar, the less it is worth today

If the discount rate increases, then the present value of a potential investment would fall.

True

Under which of the following discounting methods will the present value of an investment be the highest, assuming the same annual interest rate?

Yearly

When the discount rate:

increases, the present value of a future cash flow decreases

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.)

$16,088 Value of investment after 7 years = FV7 = $25,000Return expected from investment = i = 6.5%Duration of investment = n = 7 yearsAmount to be invested today = PV PV= FV(n)/(1+i)^n = 25,000/(1.065)^7 = Answer

What is the future value of $1,500 after 5 years if the annual return is 6%, compounded semiannually?

$2,016 Present value of the investment = PV = $1,500Return = i = 6%/2 = 3%No. of years times periods per year = n = 5 x 2 = 10 FV(10) = PV x (1+i)^n =1,500 x (1.03) ^ 10 = answer

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 pays compound interest, what will be the interest on interest in five years?

$750; $95.56 Deposit today = PV = $2,500Interest 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

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? (Round to the nearest dollar.)

$8,870 Present value of the investment = PV = $7,500Interest rate on CD = i = 5.75%No. of years = n = 3 FV3= PV × (1 + i)^n = $7,500 × (1.0575)^3= $8,869.57

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? (Round off to the nearest dollar.)

$8,885 Amount needed = FV = $16,860Interest rate = i = 5.75%Duration of investment = n = 6 yearsPresent Value = PV6 = $12,055.22 PV(6) = FV/(1+ i )^n = 16,860/(1.0575)^6 = 16,860/1.398564 = 12,055.22

At what rate must $4,000 be compounded annually for it to increase to $40,000 in 15 years? (Do not round the intermediate calculations. Round the final answer to the nearest two decimals.)

16.59% N 15 i 16.59 PV 0 PMT -4,000 FV 40,000 or Future value = Present value × (1 + interest rate)n; $40,000 = $4,000 × (1 + i)15; (1 + i)15= $40,000 / $4,000; (1 + i)15 = 10 - 1; (1 + i)15 = 10 - 1; (100.6666) - 1; r = 1.1659 - 1; Rate = 16.59%

Winston Baker will invest $25,000 in a spa that his sister is starting. He will triple his investment in six years. What is the rate of return that Winston is being promised? (Rounded to the nearest percent.)

20% Amount being invested = PV = $25,000 Amount to be paid back after 6 years = FV = $75,000 Interest rate on investment = i = ? Duration of investment = n = 6 years Present value of investment = PV PV = FV(N)/(1+i)^n (#14 quiz)

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 PV = FV(N)/(1+i)^n (#13 quiz)

If the interest rate per year and the number of years involved remain the same, the total amount of interest earned on an investment will remain the same irrespective of the frequency of compounding.

False

Starting to invest early for retirement reduces the benefits of compound interest.

False

Anne Morgan wants to borrow $6,000 for a period of four years. She has two choices. Her bank will lend her the amount at 7.25 percent compounded annually. She can also borrow from her firm and will have to repay a total of $8,130.93 at the end of four years. Should Anne choose her bank or the firm, and what is the interest rate if she borrows from her firm? (Round to the nearest percent.)

She should borrow from the bank as the firm is charging a higher interest of 8%. Amount to be borrowed = PV = $6,000Amount to be paid back after 4 years = FV = $8,130.93Interest rate on investment = i = ?Duration of investment = n = 4 yearsPresent value of investment = PV PV= FV(n)/(1+i)^n 6,000= 8,130.93/(1+i)^4 (1+i)^4 = 8,130.93/6,000 = 1.355155 (1+i) = (1.355155)^1/4 = 1.07894 i= 7.89% Since borrowing from her firm results in a loan rate of 8 percent, she should take the bank loan at 7.25 percent.

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? (Round to nearest dollar.)

$16,670 Value of investment after 3 years = FV3 = $21,000 Return expected from investment = i = 8% Duration of investment = n = 3 yearsAmount to be invested today = PV PV = FV(n)/ (1+i)^n =21,000/(1.08)^3 = 16,670.48

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? (Round to the nearest dollar.)

$20,407 Present value of the investment = PV = $15,000Return on mutual fund = i = 8%No. of years = n = 4 FV4 = PV × (1 + i)n = $15,000 × (1.08)4 = $20,407.33

The future value of $200,000 invested at a 7% annual rate, compounded quarterly for 3 years is _____. (Do not round your intermediate calculations. Round the final answer to the nearest two decimal places.)

$246,287.86 Using a financial calculator to get the Future Value of these cash flows, insert the following into a financial calculator: N 12 i 1.75 PV -200,00 PMT 0 FV 246,287.86 or Future value = Present value × (1 + interest rate)n; FV = $200,000 × (1 + 0.07/4)(4×3); $200,000 × (1.0175)12; $200,000 × 1.2314; FV = $246,287.86

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 N 3 i 12 PV -100,000 PMT 0 FV 140,492.80 or Future value = Present value × (1 + interest rate)n; FV = $100,000 × (1.12)3; FV = $100,000 × 1.4049; FV = $140,492.8. The total compound interest earned is this amount less the original investment = $140,492.8 − $100,000 = $40,492.8; the total simple interest earned is calculated as follows: simple interest per year = $100,000 × 0.12 × 3 years = $36,000. Interest earned on interest = total compound interest earned − total simple interest = $40,492.8 − $36,000 = $4,492.8.

Celesta Frank wants to go on a cruise in three years. She could earn 8 percent compounded daily in an account if she deposits the money today. She needs to have $10,000 in three years. How much will she have to deposit today? (Round to the nearest dollar.)

$7,866 Return expected from investment = i = 8%; .08/365 daily = 0.00021918 Duration of investment = n = 3 years; 3*365 = 1095 Frequency of compounding = m = 365 Target investment proceeds in 3 years = FV = $10,000 Present value of amount = PV = 10,000/(1+.00021919)^1095 = 7866.49

Castelda company issues zero coupon bonds which mature in 30 years. These bonds can be bought for $999.38 and then pay no annual interest payments, only $100,000 at maturity. What is the annual percentage cost of these bonds to the issuing company? (Do not round intermediate calculations. Round your final answer to two decimal places of percentage.)

16.59% N 30 i 16.59 PV -998.38 PMT 0 FV 100,000 Future value = Present value × (1 + interest rate)n; $100,000 = $999.38 × (1 + i)30; i = 16.59%

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 N 16.89 i 10 PV -400,00 PMT 0 FV 2,000,000 OR Future value = Present value × (1 + interest rate)n; $2,000,000 = $400,000 × (1 + 0.1)n; $200,000 / $400,000) = (1 + 0.1)n; 5 = (1.1000)n; n = 16.89 years.

Transent Foods announced that its current sales is $1,233,450 this year. The company forecasts a growth rate of 16 percent for the foreseeable future. How long will it take the firm to produce earnings of $3 million? (Round off to the nearest year.)

6 years N i 16 PMT 0 PV -$1,233,450 FV $3,000,000

Which of the following statements about the time value of money concept is true?

It means a dollar received today is worth more than a dollar received tomorrow

The value of a dollar invested at a positive interest rate grows over time but at a slower rate further into the future.

False

When the discount rate:

decreases, the present value of any future cash flow increases.

Celesta Frank wants to go on a cruise in three years. She could earn 8.2 percent compounded monthly in an account if she deposits the money today. She needs to have $10,000 in three years. How much will she have to deposit today? (Round to the nearest dollar.)

$7,826 Return expected from investment = i = 8.2% Duration of investment = n = 3 yearsFrequency of compounding = m = 12 Target investment proceeds in 3 years = FV3 = $10,000 Present value of amount = PV PV = FV(n)/[1+i/m]^mn = 10,000/[1+.082/12]^12x3 =$7,825.77