Annuities
It refers to a special form to accumulate interest over a regular payment or cash flow (C) per period.
Devon decides to save money for her retirement by depositing C=$524 each month in an account that is expected to earn interest with an APR of r=5.25% compounded monthly.
We will calculate the future value (FV) of her investment over a period of n=40 years.
The future value can be calculated with the formula:
[tex]FV=C\cdot\frac{(1+i)^n-1}{i}[/tex]
Where i is the interest rate adjusted for the compounding period. Since there are 12 months in one year:
[tex]i=\frac{r}{12}=\frac{0.0525}{12}=0.004375[/tex]
The number of periods is also adjusted for monthly compounding:
n = 40*12 = 480
Now apply the formula:
[tex]FV=524\cdot\frac{(1+0.004375)^{480}-1}{0.004375}[/tex]
Calculating:
[tex]\begin{gathered} FV=524\cdot1,629.45 \\ FV=853,832.69 \end{gathered}[/tex]
There will be $853,832.69 in Devon's retirement account in 40 years
