Question

how much money will be in Devon's retirement account if she continues to make the same monthly investment for 40 years

Answer 1

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:

`FV=C\cdot((1+i)^n-1)/(i)`

Where i is the interest rate adjusted for the compounding period. Since there are 12 months in one year:

`i=(r)/(12)=(0.0525)/(12)=0.004375`

The number of periods is also adjusted for monthly compounding:

n = 40*12 = 480

Now apply the formula:

`FV=524\cdot((1+0.004375)^(480)-1)/(0.004375)`

Calculating:

`\begin{gathered} FV=524\cdot1,629.45 \\ FV=853,832.69 \end{gathered}`

There will be $853,832.69 in Devon's retirement account in 40 years