Saving $60 per month for 8 years in an account earning 4.4% APR compounded monthly — what is the final balance?

Step-by-step solution

1. 1

   Find the monthly rate. APR compounded monthly means dividing by 12:

   $\frac{r}{n} = \frac{0.044}{12} \approx 0.0036666667$

2. 2

   Count the deposits. $12$ per year for $8$ years:

   $nt = 12 \times 8 = 96$

3. 3

   Use the future value of an annuity formula. Equal deposits at regular intervals is exactly the ordinary-annuity case:

   $FV = PMT \cdot \frac{\left(1 + \frac{r}{n}\right)^{nt} - 1}{\frac{r}{n}}$

4. 4

   Substitute and evaluate. $(1.0036666667)^{96} \approx 1.420993$, so

   $FV = 60 \cdot \frac{1.4209935 - 1}{0.0036666667} = 60 \cdot 114.8163955 \approx 6{,}888.98$

   Note that only 60 \times 96 = \5{,}760$was deposited — the remaining$$1{,}128.98$ is interest.