How to solve Loans — amortization schedule: outstanding balance, interest/principal split, total interest questions on Exam FM?

Question

A loan is repaid by level end-of-period payments of $2000$ over $n = 26$ periods at an effective rate of $2.67\%$ per period. Calculate the interest portion of the $10$th payment.

Accepted Answer

Formula
For level payment $P$, $L=P a_{\overline n|}$. After payment $k$, the prospective balance is $B_k=P a_{\overline{n-k}|}$, while interest in the next payment is $iB_k$.

Why this formula applies
Use the retrospective balance recursion: prior balance earns interest, then the payment is applied. Interest is the yield-rate charge on the opening balance and principal is payment minus interest.

Substitution and calculation
Here $v = 1/(1+i)$ and $a_{\overline{m}|} = (1-v^m)/i$. $B_{9} = P\,a_{\overline{n-k+1}|} = 27045.7625$, so $I_{10} = i\,B_{9} = 0.0267\cdot 27045.7625 = 722.1219$. Requested value: $722.1219$.

Answer
The answer is 722.1219, option (A).

How to Solve Loans — amortization schedule: outstanding balance, interest/principal split, total interest Questions on Exam FM

Unlock Full Step-by-Step Solution & Practice