Use the Loan Payoff Table to determine both the finance charge and the payment required to amortize a loan of $$ \$ 4700 $$ at an annual interest rate of $$ 11 \% $$ with a term of 36 monthly payments. Click the icon to view the Loan Payoff Table. The amount of each payment is $$ \$ \square $$. (Round to the nearest cent as needed.) The finance charge is $$ \$ \square $$

Question

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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.

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