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

nism-series-xb-retirement-corpus-required-15-year-annuity-due[ INVESTMENT ADVISER (LEVEL 2) ]

Mr. Z has current monthly living expenses of Rs. 40,000 (Rs. 4,80,000 p.a.) at age 52. Inflation is 10% p.a. until retirement at age 60 (8 years). Post-retirement, his portfolio yields 11% p.a. and inflation continues at 10% p.a. What corpus is required at age 60 to sustain his living expenses at the beginning of each year for 15 years in retirement?

[ A ]Rs. 1,38,61,919

[ B ]Rs. 1,44,96,632[ CORRECT ]

[ C ]Rs. 1,52,39,389

[ D ]Rs. 1,52,54,894

Takeaway

Using an annuity-due (beginning-of-year) present value calculation on the inflation-adjusted expense stream, the corpus required at age 60 is Rs. 1,44,96,632, so option B is correct.

Derivation

Step 1: Living expense at retirement = FV(10%, 8, , -4,80,000) = Rs. 10,28,922.63. Step 2: Real rate post-retirement = ((1.11)/(1.10)) - 1 = 0.90909%. Step 3: PV of a 15-year annuity due (Type 1, since expenses are needed at the start of each year) = PV(0.90909%, 15, -1028922.63, 0, 1) = Rs. 1,44,96,632. The 'annuity due' setting is the crux of this question — a retiree needs money on day one of each year to live on, not at year-end, so using Type 0 systematically understates the required corpus.

Why the others fail

A — Rs. 1,38,61,919

Uses an ordinary annuity (Type 0, end-of-year payment) instead of an annuity due, which leaves the retiree without funds to spend at the start of Year 1 of retirement.

C — Rs. 1,52,39,389

Assumes a lower discount rate or a higher inflation figure than the stated 11% return and 10% inflation, inflating the required corpus beyond the correct value.

D — Rs. 1,52,54,894

Represents an unadjusted nominal PV calculation that ignores the real (inflation-adjusted) compounding rate, applying the wrong discount basis entirely.