Question

You need $500,000 in 11 years. Assuming you earn 9% on your investments, how much must you invest each year? Show calculations.

Answer 1

Solution:

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

FV = P * [ [ ( 1 + r ) n - 1 ] / r ]

Where

FV = Future value ; 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

FV = $ 500,000    ; r = 9 % = 0.09   ;   n = 11   ; P = To find

Applying the above values in the formula we have:

$ 500,000 = P * [ [ ( 1 + 0.09 ) 11 - 1 ] / 0.09 ]

$ 500,000 = P * [ [ ( 1.09 ) 11   - 1 ] / 0.09 ]

$ 500,000 = P * [ [ 2.580426 - 1 ] / 0.09 ]

$ 500,000 = P * [ 1.580426 / 0.09 ]

$ 500,000 = P * 17.560293

P = $ 500,000 / 17.560293

P = $ 28,473.328368

P = $ 28,473.3284

P = $ 28,473.33 ( when rounded off to the nearest cent )

Thus the amount to be invested each year is $ 28,473.33 in order receive $ 500,000 in 11 years assuming the annual investment earns 9 % .

Note: The value of ( 1.09 ) 11 is calculated using the Excel function =POWER(Number,Power)

=POWER(1.09,11)= 1.580426