Q.Find the future value of an ordinary annuity of ₹5,000 paid at the end of every year for 4 years, at 10% per annum compound interest. [Given $(1.1)^4 = 1.4641$]

This is a direct application of the future-value-of-an-ordinary-annuity formula with $P=5000$, $i=0.10$, $n=4$.

$A = 5000\left[\dfrac{1.4641-1}{0.10}\right] = 5000(4.641) = 23{,}205$.

Step 1 — Identify the values. $P=5000$, $i=0.10$, $n=4$.

Step 2 — Apply the formula.

Step 3 — Substitute $(1.1)^4=1.4641$.

Independent check (year-by-year accumulation). Instalment 1 (paid end of year 1) earns interest for 3 more years: $5000(1.1)^3 = 5000(1.331)=6655$. Instalment 2 earns for 2 years: $5000(1.1)^2=5000(1.21)=6050$. Instalment 3 earns for 1 year: $5000(1.1)=5500$. Instalment 4 (paid at the very end) earns no interest: $5000$. Total: $6655+6050+5500+5000=23{,}205$ — matches the formula result exactly.

The year-by-year accumulation in the Independent check is a completely formula-free way to solve small-$n$ annuity problems and is a reliable cross-check on the closed-form formula for any $n$.

Using the annuity-due formula (multiplying by an extra $(1+i)$) when the question specifies instalments paid at the end of each year is a common mix-up — always confirm from the wording whether payments are at the beginning (due) or end (ordinary/immediate) of each period before choosing the formula.