FIN 320F Unit 6 Quiz

Starlite Industries will need $2.2 million 4.5 years from now to replace some equipment. Currently, the firm has some extra cash and would like to establish a savings account for this purpose. The account pays 3.6 percent interest, compounded annually. How much money must the company deposit today to fully fund the equipment purchase?

$1,876,306.49 Present value = $2,200,000/(1 + .036)4.5= $1,876,306.49

You want to buy a new sports coupe for $84,600and the finance office at the dealership has quoted you an APR of 7.1 percent, compounded monthly, for 72 months. How much interest will you pay over the life of the loan assuming you make all payments on a timely basis?

$19,542 PV = $84,600 = C × [(1 - {1 / [1 + (.071 / 12)]72}) / (.071 /.12)] C = $1,446.41 Total interest = ($1,446.41 × 72) - $84,600 = $19,542

Compass Bank is offering an APR of.8 percent, compounded daily, on its savings accounts. If you deposit $2,500 today, how much will you have in the account in 15 years?

$2,818.74 FV = $2,500 ×[1 + (.008/365)]5,475 = $2,818.74

Eulis Co. has identified an investment project with the following cash flows. Year Cash Flow 1 $ 1,210 2 1,120 3 1,550 4 1,910 What is the present value at 23 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

$3,391.46 To solve this problem, we must find the PV of each cash flow and add them. To find the PV of a lump sum, we use: PV = FV / (1 + r)t PV@23% = $1,210 / 1.23 + $1,120 / 1.232 + $1,550 / 1.233 + $1,910 / 1.234 = $3,391.46

Capstone Investments is considering a project that will produce cash inflows of $11,000 at the end of Year 1, $24,000 in Year 2, and $36,000 in Year 3. What is the present value of these cash inflows at a discount rate of 12 percent?

$54,578.17 PV = ($11,000/1.12) + ($24,000/1.122) + ($36,000/1.123) = $54,578.17

Kevin just deposited $13,000 into his savings account at Traditions Bank. The bank will pay .87 percent interest, compounded annually, on this account. How much interest on interest will he earn over the next 5 years?

$9.93 Interest on interest = $13,000 ×(1 + .0087)5- [$13,000 + ($13,000 ×.0087 ×5)] = $9.93

Your coin collection contains 80 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 2048, assuming they appreciate at an annual rate of 5.2 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

10,389.65 ± .1% To find the FV of a lump sum, we use: FV = PV(1 + r)t FV = $80(1.052)96 FV = $10,389.65

You have just received notification that you have won the $2.19 million first prize in the Centennial Lottery. However, the prize will be awarded on your 100th birthday (assuming you're around to collect), 61 years from now. What is the present value of your windfall if the appropriate discount rate is 12 percent? (Enter your answer in dollars, not millions, e.g., 1,234,567. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

2,178.44 ± .1% To find the PV of a lump sum, we use: PV = FV / (1 + r)t PV = $2,190,000 / 1.1261 PV = $2,178.44

Stephen claims that he invested $6,000 six years ago and that this investment is worth $28,700 today. For this to be true, what annual rate of return did he have to earn? Assume the interest compounded annually.

29.80 percent $28,700 = $6,000 ×(1 + r)6 r = 29.80 percent

Eulis Co. has identified an investment project with the following cash flows. Year Cash Flow 1 $ 1,210 2 1,120 3 1,550 4 1,910 What is the present value at 17 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

3,839.41 ± 0.1% To solve this problem, we must find the PV of each cash flow and add them. To find the PV of a lump sum, we use: PV = FV / (1 + r)t PV@17% = $1,210 / 1.17 + $1,120 / 1.172 + $1,550 / 1.173 + $1,910 / 1.174 = $3,839.41

Which one of the following has the highest effective annual rate?

6 percent compounded daily

Lisa has $1,000 in cash today. Which one of the following investment options is most apt to double her money?

8 percent interest for 9 years

What is the future value of $1,640 in 16 years assuming an interest rate of 11 percent compounded semiannually? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

9,097.51 ± 0.1% For this problem, we need to find the FV of a lump sum using the equation: FV = PV(1 + r)t It is important to note that compounding occurs semiannually. To account for this, we will divide the interest rate by two (the number of compounding periods in a year), and multiply the number of periods by two. Doing so, we get: FV = $1,640[1 + (.110 / 2)]32 FV = $9,097.51

Which one of the following will increase the present value of a lump sum future amount to be received in 15 years?

A decrease in the interest rate

First City Bank pays 7 percent simple interest on its savings account balances, whereas Second City Bank pays 7 percent interest compounded annually. If you made a deposit of $16,000 in each bank, how much more money would you earn from your Second City Bank account at the end of 11 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Difference $ 5,357.63 ± 0.1% The simple interest per year is: $16,000 × .07 = $1,120 So, after eleven years, you will have: $1,120 × 11 = $12,320 in interest. The total balance will be: Total balance = $16,000 + 12,320 Total balance = $28,320 With compound interest, we use the future value formula: FV = PV(1 + r)^t FV = $16,000(1.07)11 FV = $33,677.63 The difference is: Difference = $33,677.63 - 28,320 Difference = $5,357.63

Which one of the following can be classified as an annuity but not as a perpetuity?

Equal annual payments for life

Investment X offers to pay you $4,700 per year for 9 years, whereas Investment Y offers to pay you $6,400 per year for 5 years. If the discount rate is 8 percent, what is the present value of these cash flows? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

Investment X $ 29,360.37 correct Investment Y $ 25,553.00 correct To find the PVA, we use the equation: PVA = C({1 - [1 / (1 + r)t]} / r) At an interest rate of 8 percent: X@8%: PVA = $4,700{[1 - (1 / 1.089) ] / .08 } = $29,360.37 Y@8%: PVA = $6,400{[1 - (1 / 1.085) ] / .08 } = $25,553.34

Investment X offers to pay you $4,700 per year for 9 years, whereas Investment Y offers to pay you $6,400 per year for 5 years. If the discount rate is 20 percent, what is the present value of these cash flows? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

Investment X 18,945.54 ± 0.1% Investment Y 19,139.92 ± 0.1% And at an interest rate of 20 percent: X@20%: PVA = $4,700{[1 - (1 / 1.209) ] / .20 } = $18,945.54 Y@20%: PVA = $6,400{[1 - (1 / 1.205) ] / .20 } = $19,139.92

Eulis Co. has identified an investment project with the following cash flows. Year Cash Flow 1 $ 1,210 2 1,120 3 1,550 4 1,910 If the discount rate is 9 percent, what is the present value of these cash flows?

Present value $ 4,602.75 To solve this problem, we must find the PV of each cash flow and add them. To find the PV of a lump sum, we use: PV = FV / (1 + r)t PV@9% = $1,210 / 1.09 + $1,120 / 1.092 + $1,550 / 1.093 + $1,910 / 1.094 = $4,602.75

Jamie earned $14 in interest on her savings account last year. She has decided to leave the $14 in her account so that she can earn interest on the $14 this year. The interest earned on last year's interest earnings is called:

interest on interest.