Question

You invest $3108 at the beginning of every year and earn an annual rate of return of 6.4%, how much will you have in your account after 35 years? (Show your answer to the nearest cent. DO NOT round until after all calculations have been completed and you have reached your final answer.).

Answer 1

Solution:

The formula for calculating the Future value of annual savings made at the beginning of each year for "n" years, at an annual rate of return of "r" is

FV = A * [ ( ( 1 + r )ⁿ – 1 ) / r ] * ( 1 + r )

Where

FV = Future value of savings ; A = Annual amount of investment   ; r = annual rate of return   ;  n = No. of years   ;

As per the information given in the question we have

A = $ 3,108   ;   r = 6.4 % = 0.064 ;   n = 35 years   ;

Applying the above information in the formula we have

= $ 3,108 * [ ( ( 1 + 0.064 )³⁵ – 1 ) / 0.064 ] * ( 1 + 0.064 )

= $ 3,108 * [ ( ( 1.064 )³⁵ – 1 ) / 0.064 ] * 1.064       

= $ 3,108 * [ ( 8.769139 – 1 ) / 0.064 ] * 1.064

= $ 3,108 * [ 7.769139 / 0.064 ] * 1.064

= $ 3,108 * 121.392805 * 1.064

= $ 401,435.322171

= $ 401,435.32 ( when rounded off to the nearest cent )

Thus the Future value of an investment of $ 3,108 at the beginning of each year for 35 years if the annual rate of return is 6.4 % is = $ 401,453.32

Note: The value of ( 1.064 ) ³⁵   is calculated using the Excel function =POWER(Number,Power)

=POWER(1.064,35) = 8.769139