Answer:
A = $5,561
Step-by-step explanation:
Compound Interest
It occurs when the interest is reinvested instead of 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\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
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The investment is given as P=$500 at a compound interest of r=12.8%=0.128. Since the compounding period is not given, we assume n=1 (once per year). We are required to calculate the money in the account after t=20 years.
Substituting:
[tex]{\displaystyle A=\$500\left(1+{\frac {0.128}{1}}\right)^{1*20}}[/tex]
[tex]{\displaystyle A=\$500\left(1.128}\right)^{20}}[/tex]
A = $5,561
