Finance - Chapter 6

You want to be a millionaire when you retire in 30 years and expect to earn 8.5 percent compounded monthly. How much more will you have to save each month if you wait 10 years to start saving versus if you start saving at the end of this month? $989.10 $1,046.80 $841.15 $808.47 $947.22

$989.10 Explanation FVA30 years = $1,000,000 = C{[(1 + .085/12)^((30)(12)) − 1]/(.085/12)} C = $605.80 FVA20 years = $1,000,000 = C{[(1 + .085/12)(20)(12) − 1]/(.085/12)} C = $1,594.90 Difference = $1,594.90 − 605.80 Difference = $989.10

The Rodriquez family is determined to purchase a $250,000 home without incurring any debt. The family plans to save $2,500 a quarter for this purpose and expects to earn 6.65 percent compounded quarterly. How long will it be until the family can purchase a home? 23.09 years 59.39 years 48.82 years 14.85 years 35.46 years

14.85 years Explanation FVA = $250,000 = $2,500({[1 + (.0665/4)]t − 1}/(.0665/4)) t = 59.39 quarters, or 14.85 years

Al's obtained a discount loan of $68,500 today that requires a repayment of $88,000, 3 years from today. What is the APR? 8.71% 8.01% 7.87% 8.90% 8.57%

8.71% Explanation $88,000 = $68,500(1 + r)3r = ($88,000/$68,500)1/3 − 1r = .0871, or 8.71%

You have been investing $300 a month for the last 8 years. Today, your investment account is worth $43,262. What is your average rate of return on your investments? 9.69% 9.36% 7.78% 8.41% 7.23%

9.69% Explanation FVA = $43,262 = $300({[1 + (r/12)]^(8)(12) − 1}/(r/12)) r = .0969, or 9.69%

You just signed a consulting contract that will pay you $27,000, $31,000, and $44,000 at the end of the next three years, respectively. What is the present value of this contract given a discount rate of 12.7 percent? $90,506 $146,006 $79,103 $140,862 $71,257

$79,103 Explanation PV = $27,000/1.127 + $31,000/1.127^2 + $44,000/1.127^3 PV = $79,103

Your local pawn shop lends money at an annual rate of 24 percent compounded weekly. What is the effective annual rate being charged on these loans? 27.56% 26.49% 25.16% 28.64% 27.05%

27.05% Explanation EAR = (1 + .24/52)^52 − 1EAR = .2705, or 27.05%

On this date last year, you borrowed $3,900. You have to repay the loan with a lump sum payment of $6,000 six years from now. What is the interest rate? 5.47% 6.35% 6.78% 5.38% 6.01%

6.35% Explanation r = ($6,000/$3,900)^1/7 − 1r = .0635, or 6.35%

What is the EAR if a bank charges you an APR of 7.65 percent compounded quarterly? 7.87% 8.38% 8.11% 7.91% 8.02%

7.87% Explanation EAR = (1 + .0765/4)^4 − 1 EAR = .0787, or 7.87%

A new sports coupe costs $41,750 and the finance office has quoted you an APR of 7.7 compounded monthly for 36 months. What is the EAR? 7.81% 7.98% 7.94% 8.13% 8.02%

7.98% Explanation EAR = (1 + .077/12)^12 − 1 EAR = .0798, or 7.98%

Assume you borrow $30,000 at an interest rate of 5.35 percent. The terms stipulate that the principal is due in full in 5 years and interest is to be paid annually at the end of each year. How much total interest will you pay on this loan assuming you pay as agreed? $7,400 $4,982 $8,500 $8,025 $1,605

$8,025 Explanation Total interest paid= $30,000(.0535)(5) Total interest paid = $8,025

Your bank pays 1.2 percent compounded daily on its savings accounts. If you deposit $7,500 today, how much will you have in your account 15 years from now? $8,204.50 $9,714.06 $9,414.14 $9,336.81 $8,979.10

$8,979.10 Explanation FV = $7,500[1 + (.012/365)](15)(365)FV = $8,979.10

You just won the magazine sweepstakes and opted to take unending payments. The first payment will be $50,000 and will be paid one year from today. Every year thereafter, the payments will increase by 2.5 percent annually. What is the present value of your prize at a discount rate of 7.9 percent? $925,925.93 $1,350,000.00 $891,006.67 $846,918.22 $1,348,409.50

$925,925.93 Explanation GPPV = $50,000/(.079 − .025) GPPV = $925,925.93

Your parents have made you two offers. The first offer includes annual gifts of $4,000, $4,500, and $5,200 at the end of each of the next three years, respectively. The other offer is the payment of one lump sum amount today. You are trying to decide which offer to accept given the fact that your discount rate is 9.7 percent. What is the minimum amount that you will accept today if you are to select the lump sum offer? $10,378 $11,325 $17,687 $18,086 $12,489

$11,325 Explanation PV = $4,000/1.097 + $4,500/1.0972 + $5,200/1.0973 PV = $11,325

Theresa adds $1,500 to her savings account on the first day of each year. Marcus adds $1,500 to his savings account on the last day of each year. They both earn 6.5 percent annual interest. What is the difference in their savings account balances at the end of 35 years? $12,127.04 $12,219.46 $12,113.33 $12,211.12 $12,093.38

$12,093.38 Explanation FVADue = $1,500[(1.06535 − 1)/.065](1.065) FVADue = $198,145.42 FVA = $1,500[(1.06535 − 1)/.065] FVA = $186,052.04 Difference = $198,145.42 − 186,052.04 Difference = $12,093.38

This morning, you borrowed $12,700 at an APR of 6.9 percent. If you repay the loan in one lump sum three years from today, how much will you have to repay? $15,808.13 $15,313.00 $15,324.60 $15,514.47 $16,441.20

$15,514.47 Explanation FV = $12,700(1.069^3) FV = $15,514.47

Sai purchased a car today at a price of $8,500. He paid $600 down in cash and financed the balance for 48 months at 5.4 percent per year compounded monthly. What is the amount of each monthly loan payment? $463.75 $183.37 $187.39 $197.29 $1,997.27

$183.37 Explanation PVA = ($8,500 − 600) = C [(1 − {1/[1 + (.054/12)]^48})/(.054/12)] C = $183.37

A preferred stock pays an annual dividend of $5.20. What is one share of this stock worth today if the rate of return is 10.44 percent? $49.81 $41.18 $39.87 $51.48 $42.90

$49.81 Explanation PV = $5.20/.1044PV = $49.81

Which one of the following statements correctly defines a time value of money relationship? Time and present value are inversely related, all else held constant. An increase in a positive discount rate increases the present value. Time and future values are inversely related, all else held constant. An increase in time increases the future value given a zero rate of interest. Interest rates and time are positively related, all else held constant

Time and present value are inversely related, all else held constant.

A Canadian consol is best categorized as a(n): amortized cash flow. discounted loan. annuity due. ordinary annuity. perpetuity.

perpetuity

You are seeking a fixed-rate mortgage of $195,000 with a term of 30 years. Your bank quotes an APR of 6.2 percent compounded monthly. You can only afford monthly payments of $1,000, so you offer to pay off any remaining loan balance at the end of the loan term in the form of a single balloon payment. What will be the amount of the balloon payment? $173,316.67 $194,480.18 $226,315.07 $232,191.91 $202,828.59

$202,828.59 Explanation PVA = $1,000[(1 − {1/[1 + (.062/12)](30)(12)})/(.062/12)] PVA = $163,273.58 Remaining principal in today's dollars = $195,000 − 163,273.58 Remaining principal in today's dollars = $31,726.42 FV = $31,726.42(1 + .062/12)(30)(12) FV = $202,828.59