Answer
The better investment is
semiannual compounding at $ 6.5\%$,
with difference in yields$\approx\$ 221$
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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For semiannual compounding at $6.5\%,$
$A=P(1+\displaystyle \frac{r}{n})^{nt}=3000(1+\frac{0.065}{2})^{2\cdot 10}\approx\$ 5687.51$
For continuous compounding at $6\%,$
$A=Pe^{rt}= 3000e^{0.06\cdot 10}\approx\$ 5466.36$
$\$ 5687.51-\$ 5466.36\approx\$ 221$
The better investment is
semiannual compunding at $ 6.5\%$,
with difference in yields$\approx\$ 221$
