Q.A loan of ₹50,000 is to be repaid in 4 equal annual instalments at 10% per annum compounded annually, the first instalment due one year after the loan is taken. Find the annual instalment and draw up the amortisation schedule.

The loan is the present value of the four future instalments, so the equal instalment comes from the capital-recovery formula, and the amortisation schedule verifies it.

Method 1 — Capital-recovery formula.

$V = 50000$, $i = 0.10$, $n = 4$.

$(1.10)^{-4} = \\dfrac{1}{1.4641} = 0.683013 \\;\\Rightarrow\\; \\dfrac{1-0.683013}{0.10} = \\dfrac{0.316987}{0.10} = 3.169865$ …

Method 2 — Amortisation schedule (cross-check). Interest each year = opening balance × 0.10; principal = 15,773.54 − interest:

Computing simple interest of ₹5,000 for all four years and adding it as a flat charge over-states the cost, because it ignores that the outstanding balance — and hence the interest — falls each year. Amortisation always charges interest only on the reducing balance, so the t …