Question

Suppose you plan to invest $5,000 each year (beginning at the end of this year) into a retirement account that will pay 15%. What will be the value of the retirement account if you plan to retire in 40 years? (Assume the retirement account has a zero balance currently) please show work.

$33,208.89

$38,190.22

$10,229,769.27

$8,895,451.54

Answer 1

Solution:

The formula for calculating the Future value of annuity at the end of n years is

= P *[ [ ( 1 + r ) ⁿ- 1 ] / r ]

Where P = Periodic Deposit i.e., Fixed amount of Annual deposit

r = rate of interest   ; n = no. of years

A per the information given in the question we have

P = $ 5,000    ; r = 15 % = 0.15   ;   n = 40   ;

Applying the above values in the formula we have:

= 5,000 * [ [ ( 1 + 0.15 ) ⁴⁰   - 1 ] / 0.15 ]                        

= 5,000 * [ [ ( 1.15 ) ⁴⁰   - 1 ] / 0.15 ]

= 5,000 * [ [ 267.863546 – 1 ] / 0.15 ]

= 5,000 * [ 266.863546 / 0.15 ]

= 5,000 * 1,779.090308

= 8,895,451.541157

= $ 8,895,451.54 ( when rounded off to two decimal places )

Thus the Solution is Option 4. $ 8,895,451.54

The value of the retirement account in 40 years = $ 8,895,451.54