Chapter 5
You feel that you will need $1.8 million in your retirement account and when you reach that amount, you plan to retire. You feel you can earn an APR of 9.8 percent compounded monthly and plan to save $245 per month until you reach your goal. How many years will it be until you reach your goal and retire?
$1,800,000 = $245{[1 - 1/(1 + .0980/12)^t]/.0980} t = 505.42 months/12 = 42.12 years
You want to retire exactly 30 years from today with $1,890,000 in your retirement account. If you think you can earn an interest rate of 9.83 percent compounded monthly, how much must you deposit each month to fund your retirement?
$1,890,000 = C[(1 + .0983/12)^360 − 1)/(.0983/12)] C = $866.92
Ken just purchased new furniture for his house at a cost of $17,100. The loan calls for weekly payments for the next 6 years at an annual interest rate of 11.41 percent. How much are his weekly payments?
$17,100 = C[1 − (1/(1 + .1141/52)^312)/(.1141/52)] C = $75.75
You have decided to buy a car that costs $24,600. Since you do not have a big down payment, the lender offers you a loan with an APR of 5.95 percent compounded monthly for 6 years with the first monthly payment due today. What is the amount of your loan payment?
$24,600 = C(1 + .0595/12)[(1 −1/(1 + .0595/12)^72)/(.0595/12)] C = $407.11
Gerritt wants to buy a car that costs $26,250. The interest rate on his loan is 5.29 percent compounded monthly and the loan is for 5 years. What are his monthly payments?
$26,250 = C[1 − (1/(1 + .0529/12)^60)/(.0529/12)] C = $498.87
You want to buy a house and will need to borrow $270,000. The interest rate on your loan is 6.07 percent compounded monthly and the loan is for 25 years. What are your monthly mortgage payments?
$270,000 = C[1 − (1/(1 + .0607/12)^300)/(.0607/12)] C = $1,751.19
Thom owes $7,000 on his credit card. The credit card carries an APR of 18.3 percent compounded monthly. If Thom makes monthly payments of $220 per month, how long will it take for him to pay off the credit card assuming that he makes no additional charges?
$7,000 = $220{[1 − 1/(1 + .183/12)^t]/.183/12} t = 43.87 months
Your credit card company charges you 1.30 percent per month. What is the APR on your credit card?
APR = 1.30% × 12 = 15.60%
Your credit card company charges you 1.47 percent per month. What is the EAR on your credit card?
EAR = (1 + .0147)^12 - 1 = .1914, or 19.14%
One year ago, the Jenkins Family Fun Center deposited $3,600 into an investment account for the purpose of buying new equipment four years from today. Today, they are adding another $5,400 to this account. They plan on making a final deposit of $7,600 to the account next year. How much will be available when they are ready to buy the equipment, assuming they earn a rate of return of 8 percent?
FV = $3,600 (1 + 0.08)^5 + $5,400 (1 + 0.08)^4 + $7,600 (1 + 0.08)^3 = $22,210.03
You have just started a new job and plan to save $4,350 per year for 38 years until you retire. You will make your first deposit in one year. How much will you have when you retire if you earn an annual interest rate of 10.73 percent?
FV = $4,350[1.1073^38 − 1)/.1073] = $1,909,173.56
Your parents are giving you $215 a month for 4 years while you are in college. At an interest rate of .35 percent per month, what are these payments worth to you when you first start college?
PV = $215[(1 −1/1.0035^(4×12))/.0035] = $9,484.46
You have just leased a car that has monthly payments of $285 for the next 3 years with the first payment due today. If the APR is 4.92 percent compounded monthly, what is the value of the payments today?
PV = $285(1.0041)[(1 −1/1.004^136) / .0041] = $9,559.67
Todd can afford to pay $435 per month for the next 7 years in order to purchase a new car. The interest rate is 7.7 percent compounded monthly. What is the most he can afford to pay for a new car today?
PV = $435[(1 −1/(1 + .077/12)^(7×12))/(.077/12)] = $28,178.74
Marko, Inc., is considering the purchase of ABC Co. Marko believes that ABC Co. can generate cash flows of $5,700, $10,700, and $16,900 over the next three years, respectively. After that time, they feel the business will be worthless. Marko has determined that a rate of return of 11 percent is applicable to this potential purchase. What is Marko willing to pay today to buy ABC Co.?
PV = $5,700/(1+0.11) + $10,700/(1.11^2) + $16,900/(1.11^3) = $26,176.63
