Question

You save $75 a month for 30 years. If you are able to earn 6% per year on your savings, how much will you have accumulated by the end of 30 years?

Assume monthly compounding.

Answer 1

FV of Annuity :

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here deposits are made at the end of the period. FV of annuity is future value of cash flows deposited at regular intervals grown at specified int rate or Growth rate to future date.

FV of Annuity = CF [ (1+r)^n - 1 ] / r
r - Int rate per period
n - No. of periods

Particulars	Amount
Cash Flow	$                 75.00
Int Rate	0.500%
Periods	360

FV of Annuity = Cash Flow * [ [ ( 1 + r ) ^ n ] - 1 ] /r
= $ 75 * [ [ ( 1 + 0.005 ) ^ 360 ] - 1 ] / 0.005
= $ 75 * [ [ ( 1.005 ) ^ 360 ] - 1 ] / 0.005
= $ 75 * [ [6.0226] - 1 ] / 0.005
= $ 75 * [5.0226] /0.005
= $ 75338.63

Amount in account after 30 Years is $ 75338.63

As it is monthly compounding, Int Rate per Month = 6% / 12

= 0.5% it can also be written as 0.005