Question

Demarcus wants to retire with 1 million in savings by the time he turns 65 he is currently 18 years old how much will he need to save each year assuming that he can get 12% annual return on his investment

Answer 1

Demarcus wants to retire with 1 million in his account by the time he turns 65. He is 18 years old now. He has still 47 years. He can earn 12% annual rate of return. We need to find out how much he need to deposit every year inorder to get 1 million at the end of retirement.

He can earn 12% return for the first year on first year deposit, and 12% for 2nd year on 1st year deposit and 1st year interest combined and so on for future years.

The deposit is assumed to be made at the beginning of each year and not at the end of each year.

To find the deposit amount, let Y be the deposit amount annually

1,000,000 = Y x [ (1+r)^n - 1]/r + Y (1+r)^n - Y

Where, r = Interest rate, n = no of years

1,000,000 = [Y x [(1+0.12)^47 - 1]/0.12 ] + Y (1+0.12)^47 - Y

1,000,000 = [ Y x [ 205.70605 - 1]/0.12] + Y(205.50605) - Y

1,000,000 = Y [1750.88375] + Y(204.70605)

Y = 1,000,000/1910.5898

Y = 523.3986

So, annual payment of $523.3986 (paid at the beginning)

Note :

If payment is to be made at end of year

Then the formula to be used is Y x [ (1+r)^n - 1]/r