a company lends $1,500,000 for 2 years at 24%...
a company lends $1,500,000 for 2 years 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.
Given $P=\$1500000$, $r = 0.24$, $n = 12$ (compounded monthly), and $t = 2$.
## Step2: Calculate the value inside the parentheses
First, calculate $1+\frac{r}{n}=1+\frac{0.24}{12}=1 + 0.02=1.02$.
## Step3: Calculate the exponent
Next, calculate $nt=12\times2 = 24$.
## Step4: Calculate the future value
Then, $A = 1500000\times(1.02)^{24}$.
Using a calculator, $(1.02)^{24}\approx1.608437$.
So, $A=1500000\times1.608437=\$2412655.5$.
## Step5: Calculate the interest
The interest $I$ is given by $I=A - P$.
$I = 2412655.5-1500000=\$912655.5$.
# Answer:
(a) $\$2412655.5$
(b) $\$912655.5$