Use the Loan Payoff Table to determine both the finance charge and the payment required to amortize a loan of
at an annual interest rate of with a term of 36 monthly payments.
Click the icon to view the Loan Payoff Table.
The amount of each payment is .
(Round to the nearest cent as needed.)
The finance charge is

Ask by Dawson Mcdonald. in the United States

Mar 17,2025

Question

Use the Loan Payoff Table to determine both the finance charge and the payment required to amortize a loan of
at an annual interest rate of with a term of 36 monthly payments.
Click the icon to view the Loan Payoff Table.
The amount of each payment is .
(Round to the nearest cent as needed.)
The finance charge is

Ask by Dawson Mcdonald. in the United States

Mar 17,2025

UpStudy AI · Accepted Answer

We start with the general formula for the monthly payment on an amortized loan:

$$
P = L \cdot \frac{r (1+r)^n}{(1+r)^n-1}
$$

where

- $$ L $$ is the principal (loan amount),
- $$ r $$ is the monthly interest rate,
- $$ n $$ is the total number of payments.

Given:
 
- $$ L = 4700 $$,
- Annual interest rate = $$ 11\% $$ so the monthly rate is

$$
r = \frac{11\%}{12} = \frac{0.11}{12} \approx 0.009166667,
$$

- $$ n = 36 $$ monthly payments.

1. Calculate $$(1+r)^n$$:

$$
(1+r)^n = \left(1+0.009166667\right)^{36}
$$

A careful computation yields

$$
(1+r)^n \approx 1.3892.
$$

2. Substitute into the formula:

$$
P = 4700 \cdot \frac{0.009166667 \times 1.3892}{1.3892-1}
$$

Compute the numerator:

$$
0.009166667 \times 1.3892 \approx 0.012748,
$$

and the denominator:

$$
1.3892 - 1 = 0.3892.
$$

Thus, the ratio is

$$
\frac{0.012748}{0.3892} \approx 0.03273.
$$

Then the monthly payment is

$$
P = 4700 \times 0.03273 \approx 153.83.
$$

So, the required payment is approximately \$$$153.83$$ per month.

3. Next, to find the total finance charge, determine the total amount paid over 36 months and subtract the original loan:

$$
\text{Total Paid} = 153.83 \times 36 \approx 5533.88,
$$

$$
\text{Finance Charge} = 5533.88 - 4700 = 833.88.
$$

Thus, the finance charge is approximately \$$$833.88$$.

Final answers:

- The monthly payment is \$$$153.83$$.
- The finance charge is \$$$833.88$$.
The monthly payment is \$153.83, and the finance charge is \$833.88.