Question

Adams Madison needs $252,800 in 10 years. How much must he invest at the end of each year, at 4% interest, to meet his needs?

Answer 1

Given,

FV = Future value = $ 252,800

n = No. of years = 10 years

r = Interest rate = 4 % p.a. = 4 % per annum = 0.04 per annum per $

Find P (= periodic payment) ?

Calculation:

FV = P [( (1+r)ⁿ -1 )/ r]

==> P = FV /  [( (1+r)ⁿ -1 )/ r] = $ 252,800 / [( (1+0.04)¹⁰ -1 ) / 0.04] = $ 21,055.95072

==> P = $ 21,055.95072 = $ 21,055.95

Therefore,

He has to invest $ 21,055.95 end of the each year to have $ 252,800 after 10 years @ 4 % p.a.

Answer: $ 21,055.95