Question

If Josh (age 41) wants to know his current income of $100,000 will grow 7% every year until he retires at age 62, what is his annual income right before he retires?

A. $186,029.46

B. $227,876.81

C. $414,056.24

Answer 1

Solution:

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

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

Where

P = Principal   ;   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

P = $ 100,000   ; r = 7 % = 0.07 ; n = 1   ;   t = (62 – 41 ) =21 years

Applying the above values in the formula we have

= $ 100,000 ( 1 + ( 0.07 / 1 ) ^{( 21 )}

= $ 100,000 ( 1 + 0.07 ) ²¹

= $ 100,000 ( 1.07 ) ²¹

= $ 100,000 * 4.1405624 = $ 414,056.24

Thus Josh’s Annual Income just before he retires will be = $ 414,056.24

The solution is Option C. $ 414,056.24

Note: The value of ( 1.07 ) ²¹   is calculated using the Excel formula =POWER(Number,Power)

=POWER(1.07,21)= 4.1405624