Find the monthly PITI Payment for Jammie based on a mortgage of at a rate of for 20 years with annual property taxes and hazard insurance
premium of and respectively.
Select one:
a.
b.
c.
d.

Ask by Horton Chandler. in the United States

Mar 21,2025

Question

Find the monthly PITI Payment for Jammie based on a mortgage of at a rate of for 20 years with annual property taxes and hazard insurance
premium of and respectively.
Select one:
a.
b.
c.
d.

Ask by Horton Chandler. in the United States

Mar 21,2025

UpStudy AI · Accepted Answer

Let the loan principal be $$ P = \$96,\!000 $$ with an annual interest rate of $$ 7.5\% $$ and term $$ T = 20 $$ years. The monthly interest rate is

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

The number of monthly payments is

$$
n = 20 \times 12 = 240.
$$

The formula for the monthly mortgage (principal and interest) payment is

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

Substitute the values:

$$
M = \frac{96,\!000 \times 0.00625}{1 - (1.00625)^{-240}}.
$$

Calculate the numerator:

$$
96,\!000 \times 0.00625 = 600.
$$

Now, compute the denominator. First, compute $$(1.00625)^{-240}$$:

Using the exponential approximation,

$$
(1.00625)^{240} \approx e^{240 \ln(1.00625)}.
$$

Since $$\ln(1.00625) \approx 0.00623$$, we have

$$
240 \ln(1.00625) \approx 240 \times 0.00623 \approx 1.4952,
$$
$$
(1.00625)^{240} \approx e^{1.4952} \approx 4.46.
$$

Thus,

$$
(1.00625)^{-240} \approx \frac{1}{4.46} \approx 0.2242.
$$

Then the denominator becomes

$$
1 - 0.2242 \approx 0.7758.
$$

So the monthly mortgage payment is

$$
M \approx \frac{600}{0.7758} \approx 772.77.
$$

Next, add the monthly cost for annual property taxes and hazard insurance. The annual cost is

$$
\$1,\!750 + \$858 = \$2,\!608.
$$

The monthly cost is

$$
\frac{2,\!608}{12} \approx 217.33.
$$

Therefore, the total monthly PITI payment is

$$
772.77 + 217.33 \approx 990.10.
$$

Rounded appropriately, this is approximately

$$
\$991.09.
$$

Thus, the correct answer is:

a. $$ \$991.09 $$
The monthly PITI payment for Jammie is approximately \$991.09.

Find the monthly PITI Payment for Jammie based on a mortgage of at a rate of for 20 years with annual property taxes and hazard insurance
premium of and respectively.
Select one:
a.
b.
c.
d.

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Arithmetic Questions

Find the monthly PITI Payment for Jammie based on a mortgage of at a rate of for 20 years with annual property taxes and hazard insurance premium of and respectively. Select one: a. b. c. d.

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Arithmetic Questions

Find the monthly PITI Payment for Jammie based on a mortgage of at a rate of for 20 years with annual property taxes and hazard insurance
premium of and respectively.
Select one:
a.
b.
c.
d.