Find the monthly payment and estimate the remaining balance. Assume interest is on the unpaid balance.
3 -year computer loan for at ; remaining balance after 2 years.
The monthly payment is . (Round to the nearest cent as needed.)

Ask by Cook Franklin. in the United States

Mar 20,2025

Question

Find the monthly payment and estimate the remaining balance. Assume interest is on the unpaid balance.
3 -year computer loan for at ; remaining balance after 2 years.
The monthly payment is . (Round to the nearest cent as needed.)

Ask by Cook Franklin. in the United States

Mar 20,2025

UpStudy AI · Accepted Answer

**Step 1. Determine the monthly interest rate and number of payments**

- Principal: $$ P = 2718 $$
- Annual interest rate: $$ 5.5\% $$
- Monthly interest rate: 
  $$
  r = \frac{0.055}{12} \approx 0.00458333
  $$
- Total number of months (3 years): 
  $$
  n = 3 \times 12 = 36
  $$

**Step 2. Compute the monthly payment**

The formula for the monthly payment is:
$$
M = \frac{P \, r \, (1+r)^n}{(1+r)^n - 1}
$$
First, compute $$(1+r)^n$$:
$$
(1+r)^n = (1.00458333)^{36} \approx 1.179
$$
Substitute the values:
$$
M = \frac{2718 \times 0.00458333 \times 1.179}{1.179 - 1} 
$$
Calculate the numerator:
$$
2718 \times 0.00458333 \approx 12.45,\quad 12.45 \times 1.179 \approx 14.67
$$
Calculate the denominator:
$$
1.179 - 1 = 0.179
$$
Thus, the monthly payment is:
$$
M \approx \frac{14.67}{0.179} \approx 81.94
$$
So, the monthly payment is approximately $$ \$81.94 $$.

**Step 3. Estimate the remaining balance after 2 years (24 payments)**

Let $$ t = 24 $$ be the number of months paid. The remaining balance after $$ t $$ payments is given by:
$$
B = P(1+r)^t - M \cdot \frac{(1+r)^t - 1}{r}
$$
Compute $$(1+r)^t$$ for $$ t = 24 $$:
$$
(1+r)^{24} = (1.00458333)^{24} \approx 1.116
$$
Now, substitute the values:
$$
B = 2718 \times 1.116 - 81.94 \times \frac{1.116 - 1}{0.00458333}
$$
Calculate the first term:
$$
2718 \times 1.116 \approx 3033.29
$$
Next, the fraction:
$$
\frac{1.116 - 1}{0.00458333} = \frac{0.116}{0.00458333} \approx 25.3
$$
Then, the second term:
$$
81.94 \times 25.3 \approx 2073.98
$$
Finally, the remaining balance:
$$
B \approx 3033.29 - 2073.98 \approx 959.31
$$

**Answer**

The monthly payment is $$ \$81.94 $$ and the remaining balance after 2 years is approximately $$ \$959.31 $$.
The monthly payment is \$81.94, and the remaining balance after 2 years is approximately \$959.31.

Find the monthly payment and estimate the remaining balance. Assume interest is on the unpaid balance.
3 -year computer loan for at ; remaining balance after 2 years.
The monthly payment is . (Round to the nearest cent as needed.)

Solución de inteligencia artificial de Upstudy

Responder

Solución

Bonus Knowledge

preguntas relacionadas

Latest Economics Questions

Find the monthly payment and estimate the remaining balance. Assume interest is on the unpaid balance. 3 -year computer loan for at ; remaining balance after 2 years. The monthly payment is . (Round to the nearest cent as needed.)

Solución de inteligencia artificial de Upstudy

Responder

Solución

Bonus Knowledge

preguntas relacionadas

Latest Economics Questions

Find the monthly payment and estimate the remaining balance. Assume interest is on the unpaid balance.
3 -year computer loan for at ; remaining balance after 2 years.
The monthly payment is . (Round to the nearest cent as needed.)