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

nism-series-xb-future-value-single-year-retirement-contribution[ INVESTMENT ADVISER (LEVEL 2) ]

In Case 1, Mr. Z's first-year retirement contribution is Rs. 1,29,600 (at age 53, 7 years before retirement). Invested at 8% p.a. in debt, what is the future value of this single contribution at age 60?

[ A ]Rs. 2,22,112[ CORRECT ]

[ B ]Rs. 1,86,624

[ C ]Rs. 2,02,176

[ D ]Rs. 2,46,791

Takeaway

Mr. Z's first-year retirement contribution of Rs. 1,29,600, compounded at 8% p.a. for the remaining 7 years to retirement, grows to Rs. 2,22,112, so option A is correct.

Derivation

FV = PV x (1 + r)^n = Rs. 1,29,600 x (1.08)^7. The compounding factor (1.08)^7 equals 1.713824, giving FV = Rs. 2,22,111.62, rounding to Rs. 2,22,112. Because this contribution is made at age 53 — one year into the 8-year accumulation period — it has only 7 remaining years to compound before retirement at age 60, not the full 8 years used for the initial lump-sum corpus. This tests whether candidates correctly track the diminishing compounding period for each successive year's contribution, a detail that is easy to get wrong when contributions are made partway through a multi-year accumulation schedule.

Why the others fail

B — Rs. 1,86,624

This is the nominal, un-compounded contribution amount made at age 55 (Year 3), not the future value of the age-53 contribution being asked about here.

C — Rs. 2,02,176

Calculated using simple interest: Rs. 1,29,600 x (1 + 0.08 x 7), which ignores the effect of annual compounding.

D — Rs. 2,46,791

This is the future value of the Year 2 contribution compounded for 6 remaining years, not the Year 1 contribution compounded for 7 years.