Question

Find the present value of the annuity. Assume that all interest rates are annual rates.

If Peter can afford car payments of $245 per month for 5 years, what is the price of a car that he can afford now? Assume an interest rate of 8%.
O A. $18.701.83
OB. 518,001.83
O C. $18,551.93
OD. $17,933.73

Answer 1

$12,083.02

Explanation:

The annuity formula is ...

A = P(r/12)/(1 -(1 +r/12)^(-12t))

Where P is the present value, r is the annual rate, and t is the number of years. A is the monthly payment.

For your numbers, you have ...

$245 = P(.08/12)/(1 -(1 +.08/12)^(-12·5)) = P·0.0202763943

P = $245/0.0202763943 = $12,083.02

_____

The answer choices match payment periods between 8 and 9 years. At 245 per month for 5 years, the sum of payments is only $14,700, so the loan amount must be less than that.

This is a good one to ask your teacher about.