for the following installment loan, use the accompanying apr table to determine a) the finance charge and b)…

for the following installment loan, use the accompanying apr table to determine a) the finance charge and b) the monthly payment. amount financed annual percentage rate number of monthly payments $20,100 7.5% 48 click the icon to view the partial apr table. a) the finance charge is $ (round to the nearest cent as needed.)
Answer
Since the APR table is not provided, we'll assume we are using the formula - based approach for an installment - loan finance charge and payment calculation.
Explanation:
Step1: Calculate the monthly interest rate
The annual percentage rate (APR) is $r = 7.5%=0.075$. The monthly interest rate $i=\frac{r}{12}=\frac{0.075}{12}=0.00625$.
Step2: Calculate the number of payments
The number of monthly payments $n = 48$.
Step3: Use the formula for the monthly - payment of an installment loan
The formula for the monthly payment $M$ of a loan of amount $P$ is $M=P\times\frac{i(1 + i)^n}{(1 + i)^n-1}$, where $P = 20100$. First, calculate $(1 + i)^n=(1 + 0.00625)^{48}$. Let $x=(1 + 0.00625)^{48}$. Using the formula $a^b=e^{b\ln(a)}$, we have $\ln(x)=48\times\ln(1.00625)\approx48\times0.00623=0.29904$. So, $x = e^{0.29904}\approx1.34885$. Then, $\frac{i(1 + i)^n}{(1 + i)^n-1}=\frac{0.00625\times1.34885}{1.34885 - 1}=\frac{0.0084303125}{0.34885}\approx0.024165$. $M = 20100\times0.024165=485.7165$.
Step4: Calculate the total amount paid
The total amount paid over 48 months is $T = M\times n=485.7165\times48 = 23314.4$.
Step5: Calculate the finance charge
The finance charge $FC=T - P$. $FC=23314.4-20100=3214.4$
Answer:
a) The finance charge is $$3214.40$