Answer
a. $\$ 13,116.51$
b. $\$ 13,140.67$
c. $\$ 13,157.04$
d. $\$ 13,165.31$
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: $A=Pe^{rt}$.
------------------------
a.
$A=10,000(1+\displaystyle \frac{0.055}{2})^{2\cdot 5}\approx\$ 13,116.51$
b.
$A=10,000(1+\displaystyle \frac{0.055}{4})^{4\cdot 5}\approx\$ 13,140.67$
c.
$A=10,000(1+\displaystyle \frac{0.055}{12})^{12\cdot 5}\approx\$ 13,157.04$
d.
$A=10,000e^{0.055\cdot 5}\approx\$ 13,165.31$
