Q.A person deposits ₹5,000 at the end of every year into an account paying 10% per annum compounded annually. What amount will have accumulated immediately after the 4th deposit?

This is the future value (amount) of an ordinary annuity, since equal deposits are made at the end of each year and we value the fund at the date of the last deposit.

With $(1.1)^4 = 1.4641$, the annuity factor is $4.641$, so the accumulated amount is $5000\\times4.641$.

Method 1 — Future-value annuity formula.

Here $P = 5000$, $i = 0.10$ per year, $n = 4$ (an ordinary annuity — deposits at year-end).

Method 2 — Payment-by-payment cross-check. Value each deposit at the date of the 4th deposit, so the 1st deposit earns interest for 3 years, the 2nd for 2 years, the 3rd for 1 year, and the 4th for none:

$6655+6050+5500+5000 = 23{,}205$, identical to the formula — the annuity formula is simply this sum written compactly.

A common error is to let the last deposit also earn a year's interest. In an ordinary annuity the final deposit is made at the very moment the fund is valued, so it earns no interest at all; only the earlier deposits do. Applying the annuity-due multiplier $(1+i)$ here — which would give 23,205 × 1.1 = 25,525.5 — is wrong because the deposits are at year-end, not in advance.