Answer
$\$ 8$
Work Step by Step
After $t$ years, the balance, $A$, in an account with principal $P$ and annual
interest rate $r$ (in decimal form) is given by one of the following formulas:
1. For $n$ compoundings per year: $A=P(1+\displaystyle \frac{r}{n})^{nt}$
2. For continuous compounding: $A=Pe^{rt}$.
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Continuous compounding:
$A=8000e^{0.08\cdot 3}\approx 10,169.99$
Monthly compounding:
$A=8000(1+\displaystyle \frac{0.08}{12})^{13\cdot 3}\approx 10,161.90$
10,169.99-10,161.90$=\$ 8.09$
Continuous compounding returns $\$ 8$ (rounded) more in interest.
