find the interest earned on $25,000 invested for 6 years at 7% interest compounded as follows.\na…
find the interest earned on $25,000 invested for 6 years at 7% interest compounded as follows.\na. annually\nb. semiannually (twice a year)\nc. quarterly\nd. monthly\ne. continuously\na. compounding annually, the interest earned is $12518.26. (round to the nearest cent as needed.)\nb. compounding semiannually, the interest earned is $ (round to the nearest cent as needed.)
Answer
Explanation:
Step1: Recall compound - interest formula
The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), $n$ is the number of times interest is compounded per year, $t$ is the number of years, and $A$ is the amount of money accumulated after $n$ years, including interest. The interest earned $I=A - P$. Given $P = 25000$, $r=0.07$, and $t = 6$. When compounding semiannually, $n = 2$.
Step2: Calculate the amount $A$
First, substitute the values into the formula: $A=25000(1 +\frac{0.07}{2})^{2\times6}=25000(1 + 0.035)^{12}$. Calculate $(1 + 0.035)^{12}\approx1.5116019$. Then $A = 25000\times1.5116019=37790.0475$.
Step3: Calculate the interest $I$
$I=A - P=37790.0475-25000 = 12790.0475\approx12790.05$.
Answer:
$12790.05$