Question

Your parents will retire in 20 years. They currently have $300,000 saved, and they think they will need $950,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds? Round your answer 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 of Investment   ; P =Initial Investment ;   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 = $ 950,000   ; P = $ 300,000   ;     n = 1 ( Assuming compounding is annual ) ;  

t = 20 Years ; r = To find ;

Applying the above values in the formula we have

$ 950,000 = $ 300,000 * ( 1 + ( r / 1 ) ) 1 * 20

$ 950,000 = $ 300,000 * ( 1 + r ) 20

$ 950,000 / $ 300,000 = ( 1 + r ) 20

3.166667 = ( 1 + r ) 20

( 3.166667 ) 1 / 20 = 1 + r

( 3.166667 ) 0.05 = 1 + r

1.059327 = 1 + r

1 + r = 1.059327

r = 1.059327 – 1

r = 0.059327

r = 5.9327 %

r = 5.93 % ( When rounded off to two decimal places )

The annual interest rate to be earned to reach the goal = 5.93 %

Note : ( 3.166667) ( 0.05 ) = 1.059327 is calculated using the excel formula =POWER(Number,Power)

=POWER(3.166667,0.05)