Question

Derek will deposit $2,687.00 per year into an account starting today and ending in year 18.00. The account that earns 11.00%. How much will be in the account 18.0 years from today?

Answer format: Currency: Round to: 2 decimal places.

unsure if I'm doing the process correctly. thanks

Answer 1

Solution :

Calculation of Future Value of an annuity due :

The formula for calculating the Future value of annuity due is

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

Where

FV = Future value of annuity ;   A = Annuity amount or periodic deposit   ;

r = discount rate   ; n = No. of years of deposit

As per the information given in the question we have

A = $ 2,687   ;   r = 11 % = 0.11 ;   n = 18 years

Applying the above information in the formula we have

= $ 2,687 * [ ( ( 1 + 0.11 )¹⁸ – 1 ) / 0.11 ] * ( 1 + 0.11 )

= $ 2,687 * [ ( ( 1.11 )¹⁸ – 1 ) / 0.11 ] * 1.11                

= $ 2,687 * [ ( 6.543553– 1 ) / 0.11 ] * 1.11

= $ 2,687 * [ 5.543553 / 0.11 ] * 1.11                           

= $ 2,687 * 50.395936 * 1.11

= $ 150,309.405386

= $ 150,309.41 ( when rounded off to two decimal places )

Thus the amount that will be available in the account 18 years from today = $ 150,309.41

Note: The value of ( 1.11 ) ¹⁸   is calculated using the Excel formula =POWER(Number,Power)

=POWER(1.11,18) = 6.543553