Compound Interest on Periodic Savings — Annuity due (deposits at the beginning of each year): Neeraj saves ₹ 400 at the beginning of each year and lends each deposit at 5% per annum, compounded yearly. What will his savings be worth at the end of 3 years?

Introduction / Context:When equal deposits are made every period and earn compound interest, the situation is an annuity. If deposits occur at the beginning of each period, it is an annuity due; each payment earns one extra period of interest compared with end-of-period deposits. The future value (FV) of an annuity due at interest rate i for n years with payment A is FV = A * [(1 + i) + (1 + i)^2 + ... + (1 + i)^n].

Given Data / Assumptions:

• Payment each year A = ₹ 400
• Interest rate i = 5% = 0.05 per annum
• Number of years n = 3
• Deposits at the beginning of each year (annuity due); evaluate value at end of year 3

Concept / Approach:The k-th deposit (counting from 1) compounds for (n − k + 1) years to the end. Thus FV = 400 * [(1.05)^3 + (1.05)^2 + (1.05)]. This is equivalent to the annuity-due formula FV = A * [((1 + i)^n − 1)/i] * (1 + i).

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• ₹ 1261.00 corresponds to end-of-year deposits (ordinary annuity), which is not the stated timing here.
• ₹ 1312.50, ₹ 1284, ₹ 1315 are near-miss values from rounding or mixed timing assumptions.

Common Pitfalls:

• Confusing beginning vs end of year deposits; timing changes the compounding periods.
• Rounding intermediate steps too early.

Final Answer:Rs. 1324.05.