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

nism-series-xb-future-value-living-expenses-at-retirement[ INVESTMENT ADVISER (LEVEL 2) ]

Mr. Z currently incurs living expenses of Rs. 40,000 per month (Rs. 4,80,000 p.a.) at age 52. With inflation projected at 10% p.a., what will be his annual living expense at the beginning of his retirement at age 60 (8 years later)?

[ A ]Rs. 8,64,000

[ B ]Rs. 9,50,000

[ C ]Rs. 12,44,160

[ D ]Rs. 10,28,923[ CORRECT ]

Takeaway

Compounding Mr. Z's current annual living expenses of Rs. 4,80,000 at 10% inflation over 8 years gives a retirement-age expense of Rs. 10,28,923, so option D is correct.

Derivation

FV = PV x (1 + r)^n = Rs. 4,80,000 x (1.10)^8. The compounding factor (1.10)^8 equals 2.1435888, giving FV = Rs. 10,28,922.63, rounding to Rs. 10,28,923. This is the foundational FV step that feeds directly into the subsequent annuity-due PV corpus calculation for Mr. Z, testing basic but precise application of compound growth over the correct 8-year pre-retirement horizon before any annuity mechanics are layered on.

Why the others fail

A — Rs. 8,64,000

Calculated using simple interest: Rs. 4,80,000 x (1 + 0.10 x 8), which ignores the effect of annual compounding over the 8-year horizon.

B — Rs. 9,50,000

This is an arbitrary rounded estimate that does not correspond to applying the FV formula with the stated 10% inflation rate over 8 years.

C — Rs. 12,44,160

Calculated using 10 years of inflation compounding instead of the stated 8-year horizon to Mr. Z's retirement at age 60.