Q.Find the amount of each equal annual instalment needed to repay a loan of ₹1,00,000 in 5 equal yearly instalments at 10% per annum compound interest. [Given $(1.1)^{-5} = 0.6209$]

The loan amount is the present value of the instalment stream; rearrange the present-value formula to solve for the instalment $P$.

Step 1 — Recognise the loan amount as a present value. The ₹1,00,000 sanctioned today must equal the present value of the 5 future instalments, so $V=1{,}00{,}000$, $i=0.10$, $n=5$.

Step 2 — Rearrange the present value formula for $P$.

Step 3 — Substitute the known values.

$P = \dfrac{1{,}00{,}000\times0.10}{1-(1.1)^{-5}} = \dfrac{10{,}000}{1-0.6209} = \dfrac{10{,}000}{0.3791} \approx 26{,}378$ …

Dividing the loan simply by the number of years (₹1,00,000/5 = ₹20,000) ignores that interest continues to accrue on the outstanding balance throughout the loan's life — this simple-division shortcut always understates the true instalment amoun …