Christie is buying a new car today and is paying a $500 cash down payment.She will finance the balance at 7.25 percent interest.Her loan requires 36 equal monthly payments of $450 each with the first payment due 30 days from today.Which one of the following statements is correct concerning this purchase?

Question

Quizplus · Accepted Answer

To compute the initial loan amount, we need to use a monthly interest rate since the payments are monthly. The monthly interest rate can be found by dividing the annual interest rate by 12: 7.25% / 12 = 0.604%. 
Using this monthly interest rate, we can use the formula for the present value of an annuity formula to find the loan amount: 
PV = PMT x [1 - (1 / (1 + r)^n)] / r
where PV is the loan amount, PMT is the monthly payment, r is the monthly interest rate, and n is the number of payments. 
Plugging in the values, we have: 
PV = $450 x [1 - (1 / (1 + 0.00604)^36)] / 0.00604 
PV = $13,123.70 
Therefore, the initial loan amount is $13,123.70 and the correct statement is D. The other statements are incorrect because the present value of the car is higher than $500, the $500 is only the down payment and not the present value of the purchase, the car loan is not an annuity due, and the future value of the loan is not equal to 36 × $450, but rather it depends on the interest rate and any additional fees or charges.

Christie Is Buying a New Car Today and Is Paying