Question

I am stuck on one of my homework questions. I am hoping someone is able to explain to me what needs to be done in order to figure out the solution. The question is:

"You want to buy a new sports car for $78661. The contract is in the form of a 63-month annuity due at a 5.99 percent APR. What will your monthly payment (in $) be?"

Answer 1

Purchase Price = $ 78661, APR = 5.99 % and Annuity Tenure = 63 months, Annuity nature is Annuity due which implies beginning of period payments, Let the monthly payments be $K

Now, the sum of the present values of the monthly payments should equal the purchase price so as to conform with the laws of one price and principle of the time value of money.

Monthly Interest Rate = 5.99 / 12 = 0.49917 %

Therefore, 78661 = K x (1/0.0049917) x [1-{1/(1.0049917)^(63)}] x (1.0049917)

78661 = K x 53.9411 x 1.0049917

K = 78661 / (53.9411 x 1.0049917) = $ 1451.03