Question

Imagine that you invest $100,000 in an account that pays 5.9% annual interest compounded monthly. What will your balance be at the end of 18 years?

Answer 1

The compound interest formula is:
`A= P(1+ (r)/(n) ) ^(nt)`
Where:
A is the amount you will have.
P is the money you are investing.
r: is the interest rate (in decimals)
n: number of times the interest is compounded per year
t: time (in years)

The first thing is converting the rate from percentage to decimal:

`(5.9)/(100) = 0.059`

Since the interest is compounded every month and a year has 12 months n=12.

Now we can replace the values in our formula:

`A=100000(1+ (0.059)/(12) ) ^((12)(18))`

We can simplify the exponents to get:

`A=100000(1+ (0.059)/(12) ) ^(216)`

Finally, we can use our calculator to get 288463.33

After 18 your balance in your bank account will be $288463.33