## 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)**

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.

## 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.

## manish said

ohh i m sorry u have already mention this.

## 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.

## venkat53 said

Can’t we solve the above question in Excel?

## venkat53 said

Dear Prashanth,

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

## udaycfpudaycfp said

Dear Prashanth,

What about if the Growing annuity is R=G then ? Which formula we should use excel ?

## Prashant Shah said

When growth is equal to rate of return, formula does not work. Use excel for the same.