Archive / Investment Adviser (Level 2) / Miscellaneous Aspects of Retirement Planning

nism-series-xb-corpus-compounding-no-withdrawals-four-years[ INVESTMENT ADVISER (LEVEL 2) ]

In Case 2, Mr. Y starts with Rs. 2,00,00,000 in an 8% p.a. yielding corpus with zero withdrawals during the first 4 years. What is the exact value of the corpus at the end of Year 4?

[ A ]Rs. 2,72,09,779[ CORRECT ]

[ B ]Rs. 2,51,94,240

[ C ]Rs. 2,64,00,000

[ D ]Rs. 2,80,00,000

Takeaway

With zero withdrawals in the first four years, Mr. Y's Rs. 2,00,00,000 corpus compounding at 8% p.a. grows to exactly Rs. 2,72,09,779 by the end of Year 4, so option A is correct.

Derivation

FV = PV x (1 + r)^n = Rs. 2,00,00,000 x (1.08)^4. The compounding factor (1.08)^4 equals 1.36048896, giving FV = Rs. 2,72,09,779.20, rounding to Rs. 2,72,09,779. This question isolates a clean, uninterrupted 4-year compounding step before the case study introduces outflows in Year 5 onward, testing whether a candidate applies the correct exponent and compounding rate cleanly before any complexity from withdrawals is layered in.

Why the others fail

B — Rs. 2,51,94,240

This is the balance at the end of Year 3 (Rs. 2 Crores x 1.08^3), one year short of the requested Year 4 closing balance.

C — Rs. 2,64,00,000

Calculated using simple interest: Rs. 2 Crores x (1 + 0.08 x 4), which ignores the effect of annual compounding.

D — Rs. 2,80,00,000

Assumes a 10% annual compounding rate instead of the stated 8% p.a. yield, overstating the four-year closing balance.