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

nism-series-xb-total-accumulated-retirement-corpus-mr-z-age-60[ INVESTMENT ADVISER (LEVEL 2) ]

In Case 1, Mr. Z and his employer contribute Rs. 9,000 monthly (Rs. 1,08,000 in the base year) towards retirement funds, growing at 20% p.a. until retirement at age 60. These contributions earn 8% p.a. in debt. Combined with his initial Rs. 12 Lakhs corpus (which grows to Rs. 22,21,116), what is the total accumulated retirement corpus available to Mr. Z at age 60?

[ A ]Rs. 48,65,914[ CORRECT ]

[ B ]Rs. 44,81,442

[ C ]Rs. 46,65,905

[ D ]Rs. 50,65,910

Takeaway

Compounding the growing annual contributions at 8% and adding the grown initial corpus gives a total accumulated retirement corpus of Rs. 48,65,914 at age 60, so option A is correct.

Derivation

The annual contributions of Rs. 1,08,000 (base year) grow at 20% p.a. and are each compounded forward at the 8% debt yield to age 60, summing to Rs. 26,44,798. Adding the grown initial corpus (Rs. 22,21,116, from the prior question's FV calculation) gives Rs. 26,44,798 + Rs. 22,21,116 = Rs. 48,65,914. This tests whether a candidate can correctly combine two separate compounding streams — a lump sum and a series of unequal, growing periodic cashflows — into one consolidated corpus figure, a structure that trips up students who compound only one leg.

Why the others fail

B — Rs. 44,81,442

Understates the total by effectively dropping the final year's contribution from the compounding schedule, omitting the amount that compounds for the shortest period.

C — Rs. 46,65,905

Compounds the contribution stream correctly in isolation but fails to apply the 8% annual reinvestment yield to the running interim balances, understating total growth.

D — Rs. 50,65,910

Overstates the corpus by assuming the base-year contribution itself was already Rs. 1,29,600 rather than the stated Rs. 1,08,000, double-counting one year's step-up.