Compound interest occurs when the interest is reinvested rather than paying it out. When it happens interest in the next period is then earned on the principal sum plus previously accumulated interest.
The formula is:
[tex]{\displaystyle A=P\mleft(1+{\frac{r}{n}}\mright)^{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
The initial deposit is P=$50
The interest rate is r=5%=0.05
Since the interest compounds annually, n=1
Substituting into the formula:
[tex]{\displaystyle A=50\mleft(1+{\frac{0.05}{1}}\mright)^{1\cdot t}}[/tex]Operating:
[tex]A=50(1.05)^t[/tex]Evaluating for t=5 years:
[tex]A=50(1.05)^5=50\cdot1.2763=63.81[/tex]The account will have $63.81 after 5 years of investment
