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.)

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$