Question

You deposited $50,000 in your mutual fund account today. You make no more deposits into your account, but 12 years from today your mutual fund account balance is $200,000. What annually compounded rate of return have you earned on your mutual fund over this time period? Enter your answer rounded to two decimal places.

Answer 1

Solution:

The formula for calculating the future value of an Investment with compound Interest is

FV = P * [ ( 1 + (r/n) ) ^{n * t} ]

Where

FV = Future value ;   P = Principal amount Invested ;   r = rate of interest   ; n = No. of compounding periods per year ;

t = Time in years

As per the information given in the question we have

FV = $ 200,000 ; P = $ 50,000   ; n = 1 year ( since annual compounding )   ;   t = 12 ; r = To find

Applying the above values in the formula we have

200,000 = 50,000 * [ ( 1 + (r/1) ) ^{1 * 12} ]                       

200,000 = 50,000 * [ ( 1 + (r/1) ) ¹² ]                            

200,000 / 50,000 = [ ( 1 + (r/1) ) ¹² ]

4 = ( 1 + (r/1) ) ¹²

( 4 ) ^1/12 = 1 + r

1 + r = ( 4 ) ^1/12

1 + r = ( 4 ) ^0.083333

1 + r = 1.122462

r = 1.122462 – 1

r = 0.122462

r = 12.2462 %

r = 12.25 % ( when rounded off to two decimal places )

Thus the annually compounded rate of return earned on the mutual fund over a 12 year time period = 12.25 %

Note : Note: The value of ( 4 ) ^0.083333   is calculated using the Excel formula =POWER(Number,Power) =POWER(4,0.083333) = 1.122462