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

nism-series-xb-leisure-expense-compounding-27-years[ INVESTMENT ADVISER (LEVEL 2) ]

In Case 4, Mr. Smart's social occasion and leisure travel expenses start at Rs. 1,00,000 p.a. at age 60 and inflate at 6% p.a. What will this annual leisure expense grow to by the final retirement year at age 87 (Year 27)?

[ A ]Rs. 2,62,000

[ B ]Rs. 4,82,235[ CORRECT ]

[ C ]Rs. 3,50,000

[ D ]Rs. 6,10,500

Takeaway

Compounding Mr. Smart's leisure expense of Rs. 1,00,000 at 6% inflation over 27 years grows it to Rs. 4,82,235 by the final retirement year, so option B is correct.

Derivation

FV = PV x (1 + r)^n = Rs. 1,00,000 x (1.06)^27. The compounding factor (1.06)^27 equals approximately 4.822349, giving FV = Rs. 4,82,235. This tests long-horizon compounding discipline over a genuinely long 27-year period, where small differences in method (simple versus compound interest, or a slightly wrong rate) produce dramatically different results — exactly the kind of divergence that makes correctly modelling multi-decade retirement expense inflation so consequential in practice.

Why the others fail

A — Rs. 2,62,000

Calculated using simple interest: Rs. 1,00,000 x (1 + 0.06 x 27), which drastically understates the true compound growth over 27 years.

C — Rs. 3,50,000

This is an arbitrary linear estimate that does not correspond to applying the FV formula with the stated 6% inflation rate over 27 years.

D — Rs. 6,10,500

Assumes an 8% inflation rate instead of the stated 6%, overstating the compounded leisure expense figure for Year 27.