Answer:
There would be $500 in the account after 15 years
Step-by-step explanation:
Compound Interest
It occurs when the interest is reinvested rather than paying it out. It's basically earning interest over interest.
The formula is:
[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]
Where:
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
Austin invested P=$200 in an account with an interest rate of r=6.1% = 0.061 (decimal) during t=15 years compounded quarterly. Since there are 4 quarters in a year, n=4. Thus, applying the formula:
[tex]{\displaystyle A=\$200\left(1+{\frac {0.061}{4}}\right)^{4*15}}[/tex]
[tex]{\displaystyle A=\$200\left(1+0.01525}\right)^{60}}[/tex]
[tex]\displaystyle A=\$200*2.47959[/tex]
A = $495.92
Rounding to the nearest ten dollars:
A = $500
There would be $500 in the account after 15 years
