how much more will an investment of $15,000 earning 5% compounded continuously for 9 years earn compared to…
how much more will an investment of $15,000 earning 5% compounded continuously for 9 years earn compared to the same investment at 5% compounded monthly for 9 years?\nthe investment that is compounded continuously will earn $ \n(round to the nearest cent as needed.)
Answer
Explanation:
Step1: Calculate continuous - compounding amount
The formula for continuous - compounding is $A = Pe^{rt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the number of years. Given $P=$15000$, $r = 0.05$, and $t = 9$. $A_{c}=15000\times e^{0.05\times9}=15000\times e^{0.45}$ $A_{c}=15000\times1.568312185\approx23524.68277$
Step2: Calculate monthly - compounding amount
The formula for compound interest is $A = P(1+\frac{r}{n})^{nt}$, where $n$ is the number of times compounded per year. For monthly compounding, $n = 12$. $A_{m}=15000\times(1 +\frac{0.05}{12})^{12\times9}=15000\times(1+\frac{0.05}{12})^{108}$ First, calculate $1+\frac{0.05}{12}\approx1.00416667$. Then $(1.00416667)^{108}\approx1.56432965$. $A_{m}=15000\times1.56432965\approx23464.94475$
Step3: Find the difference
Subtract the monthly - compounding amount from the continuous - compounding amount. $A_{c}-A_{m}=23524.68277 - 23464.94475\approx59.74$
Answer:
$59.74$