a company lends $1,500,000 for 2 years at 24%, compounded monthly to another company that manufactures tug…

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$