Maths Puzzle - 6. Calculation Of Investment Returns

Very often we invest money and we are told of some returns (either assured or likely returns). The simplest scenario is one where we invest an amount in the beginning and we get a return after say 5 or 10 years.

What is the percentage return from this interest? We should use compounded interest and not simple interest. We all know that

A=P(1+ r)ⁿ

A is the amount we receive at the end. 

P is the amount we invested at the beginning

r is interest rate (as a fraction. For example 8% = 0.08) per period

n is the number of periods. Usually period is a year

r = ( (A/P)^(1/n) ) - 1

If we have multiple investments, we calculate the rate of return r for each and compare.

Now, if a project (that has some investments and some returns) has more different amounts of investment and / or returns in different years, how do we calculate the effective rate of return?

Let's take an insurance policy as an example. It may have an investment in year 1, 2, 3 and returns in the years 4, 5, 6.

Year   Investment (Returns)

  1          100

  2          100

  3          100

  4         (120)

  5         (120)

  6         (120)

Values in bracket indicate returns. An investment of 100 is made in each of the first three years and the project returns 120 in each of the last three years. Using compound interest formula given above, how do you determine the effective rate of return?