How to solve Loans — solve for the payment, the loan amount, or the number of payments questions on Exam FM?

Question

A loan of $5,573$ is repaid by $n = 26$ level end-of-period payments at an effective rate of $2.67\%$ per period. Calculate the level payment $P$.

Accepted Answer

Formula
A level-payment loan satisfies $L=P a_{\overline n|i}=P(1-v^n)/i$; isolate the requested one of $L,P,n,i$.

Why this formula applies
Equate the loan amount with the present value of all scheduled payments at the loan rate. Solve that annuity equation for the requested payment, term, or principal.

Substitution and calculation
With $v = 1/(1+i)$ and $a_{\overline{n}|} = (1-v^n)/i$: $P = L / a_{\overline{n}|} = 5573/18.5752 = 300.0241$. Requested value: $300.0241$.

Answer
The answer is 300.0241, option (D).

How to Solve Loans — solve for the payment, the loan amount, or the number of payments Questions on Exam FM

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