The compound interest formula is: [tex]A= P(1+ \frac{r}{n} ) ^{nt} [/tex]
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:
[tex] \frac{5.9}{100} = 0.059[/tex]
Since the interest is compounded every month and a year has 12 months n=12.
Now we can replace the values in our formula:
[tex]A=100000(1+ \frac{0.059}{12} ) ^{(12)(18)} [/tex]
We can simplify the exponents to get:
[tex]A=100000(1+ \frac{0.059}{12} ) ^{216} [/tex]
Finally, we can use our calculator to get 288463.33
After 18 your balance in your bank account will be $288463.33
