Question

You want to buy a new sports car from Muscle Motors for $57,500. The contract is in the form of a 60-month annuity due at an APR of 5.9 percent. What will your monthly payment be? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Monthly payment:

Answer 1

Answer:

Present value (PV) = $57,500

Interest rate (APR) = 5.9%

Number of years = 5 years

Number of installments in a year (m) = 12        

Monthly payments (A) = ?                              

PV = A(1 - (1 + r/m)-nm)

                r/m

$57,500 =  A(1  - (1 + 0.059/12)-5x12

                          0.059/12

$57,500 = A(1 - (1 + 0.004916666667)-60

                       0.004916666667

$57,500 = A(1 - (1.004916666667)-60

                       0.004916666667  

$57,500 = A(1 - 0.745069959)

                     0.004916666667

$57,500 = A(51.85017778)

$57,500         = A

51.85017778

A = $1,108.96 per month

                               

Explanation:

In this case, we need to apply the formula for present value of an ordinary annuity on the assumption that payment is made on monthly basis. The present value, interest rate (APR), number of years and number of installments in a year were provided in the question with the exception of monthly payment. Thus, the monthly payment becomes the subject of the formula.