Q.₹1,000 is deposited at the beginning of each year for 3 years in a fund earning 10% per annum compounded annually. Find the amount at the end of 3 years, and compare it with the corresponding ordinary annuity.

Because the deposits are made in advance (at the start of each year), this is an annuity due, whose amount is the ordinary-annuity amount multiplied by one extra $(1+i)$.

The ordinary amount is $1000\\times3.31 = 3310$; multiplying by $1.1$ for advance payment gives the annuity-due amount.

Method 1 — Annuity-due formula.

$P = 1000$, $i = 0.10$, $n = 3$, payments in advance.

The annuity due (₹3,641) exceeds the ordinary annuity (₹3,310) by exactly one period's interest, because every advance payment stays invested one year longer.

Method 2 — Payment-by-payment cross-check. With advance deposits, the 1st deposit earns interest for 3 years, the 2nd for 2 years and the 3rd for 1 year:

$1331+1210+1100 = 3{,}641$, matching the formula exactly.

Forgetting the extra $(1+i)$ multiplier and reporting the ordinary-annuity amount (₹3,310) for an annuity due is the classic slip. Whenever a problem says payments are made 'in advance', 'at the beginning of each period', or names rent/premium paid ahead, the annuity-due multiplier must be applied.