FIN 3601 Ch. 6

You have just leased a car that has monthly payments of $330 for the next 3 years with the first payment due today. If the APR is 6 percent compounded monthly, what is the value of the payments today?

$10,901.67 PV = $330(1.0050)[(1 −1/1.005036) / .0050] = $10,901.67

You will receive 25 annual payments of $21,500. The first payment will be received 6 years from today and the interest rate is 7.3 percent. What is the value of the payments today?

$171,496.63 PV = $21,500[(1 −1/1.073025)/.0730] = $243,923.81 PV = $243,923.81/1.07305 = $171,496.63

You have just started a new job and plan to save $4,850 per year for 43 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 10.03 percent?

$2,898,906.51 FV = $4,850[1.100343 − 1)/.1003] = $2,898,906.51

Marko, Inc., is considering the purchase of ABC Co. Marko believes that ABC Co. can generate cash flows of $6,000, $11,000, and $17,200 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 14 percent is applicable to this potential purchase. What is Marko willing to pay today to buy ABC Co.?

$25,336.81 PV = $6,000/(1 + .14) + $11,000/(1.14)2 + $17,200/(1.14)3 = $25,336.81

One year ago, the Jenkins Family Fun Center deposited $4,800 into an investment account for the purpose of buying new equipment four years from today. Today, they are adding another $6,600 to this account. They plan on making a final deposit of $8,800 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 9 percent?

$28,098.09 FV = $4,800 (1 + 0.09)5 + $6,600 (1 + 0.09)4 + $8,800 (1 + 0.09)3 = $28,098.09

Gerritt wants to buy a car that costs $25,500. The interest rate on his loan is 5.23 percent compounded monthly and the loan is for 5 years. What are his monthly payments?

$483.91 $25,500 = C[1 − (1/(1 + .0523/12)60)/(.0523/12)] C = $483.91

Your grandparents would like to establish a trust fund that will pay you and your heirs $210,000 per year forever with the first payment one year from today. If the trust fund earns an annual return of 4.1 percent, how much must your grandparents deposit today?

$5,121,951.22 PV = $210,000/.041 = $5,121,951.22

Your parents are giving you $165 a month for 4 years while you are in college. At an interest rate of .34 percent per month, what are these payments worth to you when you first start college?

$7,296.08 PV = $165[(1 −1/1.00344×12)/.0034] = $7,296.08

What is the effective annual rate for an APR of 16.50 percent compounded monthly?

17.81% EAR = (1 + .1650/12)12 - 1 = .1781, or 17.81%

One of your customers has just made a purchase in the amount of $26,400. You have agreed to payments of $550 per month and will charge a monthly interest rate of 1.38 percent. How many months will it take for the account to be paid off?

79.23 months $26,400 = $550[(1 − 1/1.0138t) / .0138]

what is the prsent value of an ordinary annuity that pays $100 per year for 20 years if the interest rate is 10% per year?

851.36 100[(1-(1.10)^20)/.10]

the annuity present value factor for a 30 year annuity with an interest rate of 10% per year is

PVIFA= {1-(1/1.1^30)}/.10=9.4269

In almost all multiple cash flow calculations, it is implicitly assumed that the cash flows occur at the _________ of each period.

end

A traditional (non-growing) annuity consists of a _____ stream of cash flows for a fixed period of time

level

A single cash flow is also known as a:

lump sum

Most investments involve:

multiple cash flows

true or false the formula for the present value interest factor for annuities is annuity present value factor = [1-(1/(1+r)^t)]/r

true