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Time Value of Money, Part-6

Posted by Prashant Shah on August 31, 2010

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)


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.


7 Responses to “Time Value of Money, Part-6”

  1. Manish said

    Sir I have one question regarding this question fv of growing annuity.what if mr a plans to start investing 10% of yearly salary at the beginning of each year for next 25 yrs wht would be the formula in this case and wht would be the answer plz reply asap.

  2. manish said

    ohh i m sorry u have already mention this.

  3. manish said

    sir i have one question wht if savings r done at the beginning or end of each month in fv of growing annuity can u plz provide me the solution by taking the same example as above reply asap as i m going to give this exam on this tuesday.

  4. venkat53 said

    Can’t we solve the above question in Excel?

  5. venkat53 said

    Dear Prashanth,

    What about if the Growing annuity is not constant?Which formula we should use?

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