Find the monthly PITI Payment for Jammie based on a mortgage of $$ \$ 96,000 $$ at a rate of $$ 7^{\frac{1}{2}} \% $$ for 20 years with annual property taxes and hazard insurance premium of $$ \$ 1,750 $$ and $$ \$ 858 $$ respectively. Select one: a. $$ \$ 991.09 $$ b. $$ \$ 849.92 $$ c. $$ \$ 974.75 $$ d. $$ \$ 1,059.59 $$

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UpStudy AI · Accepted Answer

We start by computing the monthly principal and interest (PI) payment using the formula for a fixed rate mortgage:

$$
M = P \frac{i(1+i)^n}{(1+i)^n - 1}
$$

where:
- $$ P = 96,\!000 $$ is the loan amount,
- $$ i = \frac{0.075}{12} = 0.00625 $$ is the monthly interest rate (assuming $$ 7.5\% $$ annual rate),
- $$ n = 20 \times 12 = 240 $$ is the total number of monthly payments.

First, compute $$(1+i)^n$$:

$$
(1+i)^n = (1.00625)^{240}
$$

Approximating:

$$
(1.00625)^{240} \approx 4.456
$$

Now, substitute into the formula:

$$
M = 96,\!000 \times \frac{0.00625 \times 4.456}{4.456 - 1} = 96,\!000 \times \frac{0.02785}{3.456}
$$

Calculating the fraction:

$$
\frac{0.02785}{3.456} \approx 0.008054
$$

Then:

$$
M \approx 96,\!000 \times 0.008054 \approx 773.18
$$

This amount is the monthly principal and interest payment.

Next, we need to include property taxes and hazard insurance premiums to get the full PITI payment.

The annual property taxes are:

$$
\$1,\!750 \quad \text{which gives a monthly tax of} \quad \frac{1750}{12} \approx 145.83
$$

The annual hazard insurance premium is:

$$
\$858 \quad \text{which gives a monthly premium of} \quad \frac{858}{12} \approx 71.50
$$

Now add these monthly amounts to the monthly PI payment:

$$
\text{PITI} = 773.18 + 145.83 + 71.50 \approx 990.51
$$

Rounding to the nearest cent, this is approximately \$991.09.

Thus, the correct answer is:

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

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