Sam takes out a $$ \$ 72,000 $$ mortgage at $$ 7^{\frac{1}{2}} \% $$ for 25 years. Prepare an amortization schedule for the first 3 months. Find the loan balance after 3 payments. Select one: a. $$ \$ 71,752.22 $$ b. $$ \$ 70,966.67 $$ c. $$ \$ 68,948.27 $$ d. $$ \$ 69,895.36 $$

Question

UpStudy AI · Accepted Answer

The monthly interest rate is

$$
r = \frac{7.5\%}{12} = \frac{0.075}{12} = 0.00625.
$$

The number of monthly payments is

$$
n = 25 \times 12 = 300.
$$

The monthly payment $$A$$ for a fixed‐rate mortgage is given by

$$
A = P \times \frac{r(1+r)^n}{(1+r)^n - 1},
$$

where $$ P = \$72,\!000 $$.

Substitute the values:

$$
A = 72000 \times \frac{0.00625(1.00625)^{300}}{(1.00625)^{300} - 1}.
$$

Evaluating $$(1.00625)^{300}$$ (using logarithms or a calculator) gives approximately

$$
(1.00625)^{300} \approx 6.477.
$$

Then

$$
A \approx 72000 \times \frac{0.00625 \times 6.477}{6.477 - 1}
= 72000 \times \frac{0.04048}{5.477}
\approx 72000 \times 0.007387 \approx 531.98.
$$

Thus, the monthly payment is approximately $$\$531.98$$.

We now prepare the amortization schedule for the first 3 months.

---

**Month 1**

- **Beginning Balance:** $$\$72,\!000.00$$
- **Interest:**

$$
  72000 \times 0.00625 = 450.00.
  $$
  
- **Principal:**

$$
  531.98 - 450.00 = 81.98.
  $$
  
- **Ending Balance:**

$$
  72000 - 81.98 = 71918.02.
  $$

---

**Month 2**

- **Beginning Balance:** $$\$71,\!918.02$$
- **Interest:**

$$
  71918.02 \times 0.00625 \approx 449.49.
  $$
  
- **Principal:**

$$
  531.98 - 449.49 \approx 82.49.
  $$
  
- **Ending Balance:**

$$
  71918.02 - 82.49 \approx 71835.53.
  $$

---

**Month 3**

- **Beginning Balance:** $$\$71,\!835.53$$
- **Interest:**

$$
  71835.53 \times 0.00625 \approx 448.97.
  $$
  
- **Principal:**

$$
  531.98 - 448.97 \approx 83.01.
  $$
  
- **Ending Balance:**

$$
  71835.53 - 83.01 \approx 71752.52.
  $$

---

After 3 payments, the loan balance is approximately $$\$71,\!752.52$$. Comparing with the given options, the closest is

$$
\boxed{\$71,\!752.22},
$$

which corresponds to option (a).
After 3 payments, the loan balance is approximately \$71,752.22.

Sam takes out a mortgage at for 25 years. Prepare an amortization schedule for the first 3 months. Find the loan balance after 3 payments.
Select one:
a.
b.
c.
d.

Solución de inteligencia artificial de Upstudy

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Economics Questions

Sam takes out a mortgage at for 25 years. Prepare an amortization schedule for the first 3 months. Find the loan balance after 3 payments. Select one: a. b. c. d.