Time Value of Money, Part-6

Mr. A plans to invest 10% of his yearly salary for next 25 years, salary increases by 5% p.a. The rate of return is 12% p.a. His current salary is Rs.2,00,000 p.a. and investments are made at the end of the year.

This is the question of growing annuity where amount of investment is growing at 5% rate year on year and invested at 12% rate. We will have to use following equation as this question cannot be solved using pre-set formula of calculator.

FV = A×[(1+r)ⁿ – (1+g)ⁿ]/(r-g)

Where:

FV = Future value

A = Initial amount of investment

r = Rate of return

g = Growth rate

n = Number of years

So, in the above question amount of money Mr. A accumulates at the end of 25 years will be,

FV = 20000×[(1+0.12)²⁵ – (1+0.05)²⁵]/(0.12-0.05)

Hence, he will accumulate Rs.38,89,631 at the end of 25 years from now.

Now let’s assume that Mr. A starts investing from the beginning of the year, he will accumulate.. 

FV = A×(1+r)×[(1+r)ⁿ – (1+g)ⁿ]/ r-g

FV = 20000×1.12×[(1+0.12)²⁵ – (1+0.05)²⁵]/(0.12-0.05)

Rs. 43,56,387 is the answer. This formula of growing annuity is useful when investments are growing at a constant rate. However in case where r=g, this formula is not useful, we may have to switch over to excel.