Question

You have been investing $120 a month for the last 15 years. Today, your investment account is worth $47,341.19. What is your average rate of return on your investments? Select one: o a. 9.37% O b. 9.40% e c.9.34% • d. 9.46% e.9.42% Clear my choice

Answer 1

Let the average return be r% per month.

So, the future value of this monthly annuity is $47341.19

let the amount be deposited at the end of the period, the first amount remained invested for 1 month less than 15 years i.e. 179 months , 2nd amount remained invested for 178 month and so on and there are a total of 180 installments

=> 120* (1+r)⁽¹⁷⁹⁾ + 120* (1+r)⁽¹⁷⁸⁾ + ..... + 120 = 47341.19

Writing the terms in reverse, we have

120* + 120* (1+r)⁽²⁾ + 120* (1+r)⁽³⁾ + ..... + 120* (1+r)⁽¹⁷⁹⁾ = 47341.19

LHS is a Geometric progression with sum = a *(rⁿ-1) / (r-1) where a is the first term and r is the common ratio , n is the no of terms

=> 120 *( (1+r)^{* 180} -1 ) / ((1+r)-1 ) = 47341.19

=>   ((1+r)¹⁸⁰ -1 ) / ((1+r)-1 ) = 394.51

So, r has to be found by hit and trial method

we get r =0.78834% per month

= 0.78834 *12% per annum

= 9.46% per annum