Determine the monthly payment for the installment loan.

Question

Amount Financed (P)    Annual Percentage Rate (r)   Number of payments per year     Time in years 

$700                                     7.5%                                    12                                      1

Answer 1

Trevor, this just requires use of the standard compound interest amortization formula.

Let's do it from first principles. The present value (PV) of all the future payments, P, must equal the amount, A, of the loan. Assuming payments are made at the end of each period.

Let v = 1 / (1 + i) where i is the interest rate percent.

Let n = number of payments, P.

Therefore, A = P(v + v² + v³ + . . . + vⁿ)

= Pv (1 - vⁿ) / v . . . . . . the sum of a normal geometric series

In this question: 700 = P (1 - 1/(1 + (7.5%/12)¹²) / 1/(1 + 7.5%/12)

= P (1 - 0.00625¹²) / (1 - 0.00625)

Now, solve for P. I leave the arithmetic as an exercise for you.