MC algo 5-11 Calculating Annuity Present Values

Question

Todd can afford to pay $335 per month for the next 5 years in order to purchase a new car. The interest rate is 5.7 percent compounded monthly. What is the most he can afford to pay for a new car today?

a. $17,453.72

b. $17,201.63

c. $16,581.04

d. $23,193.64

e. $18,035.51

Answer 1

To calculate the present value of the annuity, we can use the formula:

PV = PMT * [1 - (1 + r)^(-n)] / r

Where:
PV = present value
PMT = payment per period
r = interest rate per period
n = number of periods

In this case, Todd can afford to pay $335 per month for 5 years, so PMT = $335, n = 5 years * 12 months/year = 60 months, and r = 5.7% / 12 months = 0.475% per month.

Plugging in these values into the formula:

PV = $335 * [1 - (1 + 0.475%)^(-60)] / 0.475%

PV ≈ $16,581.04

Therefore, the most Todd can afford to pay for a new car today is approximately $16,581.04.

The correct option is c. $16,581.04.