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nism-series-xa-future-value-retirement-annuity-formula[ INVESTMENT ADVISER (LEVEL 1) ]

An investor saves ₹25,000 per month (₹3,00,000 per year) into an equity mutual fund compounding at 10.0% p.a. What will be the accumulated terminal corpus at the end of 20 years?

[ A ]₹60,00,000 (Simple sum of principal contributions without compound growth)

[ B ]₹50,00,000

[ C ]Approximately ₹1,71,82,500 [ PMT * ((1 + r)^n - 1) / r ][ CORRECT ]

[ D ]₹5,00,00,000

Takeaway

Option C is correct: Approximately ₹1,71,82,500 [ PMT * ((1 + r)^n - 1) / r ]

Derivation

Annual savings PMT = ₹3,00,000 (₹25,000 × 12). The Future Value of Annuity growth factor over 20 years at 10.0% is [(1.10)^20 − 1] / 0.10 ≈ 57.275. Terminal corpus = ₹3,00,000 × 57.275 ≈ ₹1,71,82,500. Of that corpus, the investor's own contributions total just ₹60,00,000 (₹3,00,000 × 20 years) — meaning roughly ₹1.12 Crore, or nearly 65% of the final figure, comes purely from compound growth on those contributions, not from money the investor actually put in. This is the core case for starting SIPs early: the later years of a long horizon contribute disproportionately to the terminal number precisely because compounding accelerates on an already-large base.

Why the others fail

A — ₹60,00,000 (Simple sum of principal contributions without compound growth)

States only the sum of principal contributions over 20 years, ignoring roughly ₹1.12 Crore in compound growth that accrues on top of those contributions.

B — ₹50,00,000

Understates the terminal corpus by a wide margin; compounding ₹3,00,000 a year at 10.0% for 20 years correctly produces close to ₹1.72 Crore, not this figure.

D — ₹5,00,00,000

Overstates the terminal corpus well beyond what compounding ₹3,00,000 a year at 10.0% for 20 years actually produces, which comes to roughly ₹1.72 Crore.