Q.Find the future value of an annuity due of ₹4,000 paid at the beginning of every year for 3 years, at 10% per annum compound interest. [Given $(1.1)^3=1.331$]

First find the ordinary-annuity future value, then multiply by $(1+i)$ to convert it to an annuity-due value.

Ordinary annuity value $=4000\left[\dfrac{1.331-1}{0.10}\right]=4000(3.31)=13{,}240$. Annuity due $=13{,}240\times1.1=14{,}564$.

Step 1 — Find the ordinary-annuity future value first. $P=4000$, $i=0.10$, $n=3$.

Step 2 — Convert to annuity due by multiplying by $(1+i)$.

Independent check (year-by-year, each instalment now earning one extra year of interest). Instalment 1 (start of year 1) earns interest for all 3 years: $4000(1.1)^3=4000(1.331)=5324$. Instalment 2 (start of year 2) earns for 2 years: $4000(1.1)^2=4000(1.21)=4840$. Instalment 3 (start of year 3) earns for 1 year: $4000(1.1)=4400$. Total: $5324+4840+4400=14{,}564$ — matches exactly.

Applying the ordinary-annuity formula directly to a due-type problem (forgetting the extra $(1+i)$ factor) understates the true future value, since every payment in an annuity due genuinely earns one additional period of interest compared to an ordinary annuity of the same size.