a company lends $1,300,000 for 1 year at 24%,...
a company lends $1,300,000 for 1 year at 24%, compounded monthly to another company that manufactures tug boats. find (a) the future value and (b) the interest. click the icon to view the compound interest table. (a) future value = $ (simplify your answer.)
Answer
# Explanation:
## Step1: Identify 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), $n$ is the number of times compounded per year, and $t$ is the number of years.
Here, $P=\$1300000$, $r = 0.24$, $n = 12$ (compounded monthly), and $t = 1$.
## Step2: Calculate the future value
Substitute the values into the formula:
$A=1300000(1 +\frac{0.24}{12})^{12\times1}$
$A=1300000(1 + 0.02)^{12}$
First, calculate $(1 + 0.02)^{12}$. Using a calculator, $(1.02)^{12}\approx1.26824179456$.
Then, $A = 1300000\times1.26824179456\approx1648714.33$.
## Step3: Calculate the interest
The interest $I$ is given by $I=A - P$.
$I=1648714.33-1300000=\$348714.33$
# Answer:
(a) $\$1648714.33$
(b) $\$348714.33$