Question

If you invest $4,000 per year at the end of each year for the next 30 years at an interest rate of 7.5%, how much will you have accumulated at the end of the 30 years? If instead, the payments occur at the beginning of the year what will be the amount?

Answer 1

PMT = $ 4000

i = 7.5 %

n = 30 years

Total accumulated at end of the 30 years = PMT × ((1 + r)^n - 1) / r + PMT

= $ 4000 * [(1+ 0.075)²⁹ - 1] / 0.075 + 4000

= 385021

If instead, the payments occur at the beginning of the year what will be the amount =

Total = [ PMT * ((1 + r)ⁿ - 1) / r ]

= $ 4000 * [(1+ 0.075)³⁰ - 1] / 0.075

= 413597.