You purchase a home for $$ \$ 69,750 $$ at $$ 6.75 \% $$ for 30 years. The property taxes are $$ \$ 2,450 $$ per year, and the hazard insurance premium is $$ \$ 256 $$ semiannually. Find the monthly PITI payment. Select one: a. $$ \$ 699.51 $$ b. $$ \$ 594.73 $$ c. $$ \$ 1,059.40 $$ d. $$ \$ 246.83 $$

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We begin by finding the monthly principal and interest (P&I) payment. The formula for a fixed-rate mortgage is

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

where  
$$ P = 69750 $$ (the purchase price),  
$$ r = \frac{6.75\%}{12} = \frac{0.0675}{12} \approx 0.005625 $$ (monthly interest rate), and  
$$ n = 30 \times 12 = 360 $$ (total number of monthly payments).

Thus, the monthly P&I is

$$
M = 69750 \cdot \frac{0.005625 (1+0.005625)^{360}}{(1+0.005625)^{360} - 1}.
$$

While the exact computation would use a calculator, performing an approximation gives a P&I roughly around \$452.47.

Next, we compute the monthly property tax. The annual property tax is

$$
\text{Annual Tax} = 2450,
$$

so the monthly tax is

$$
\text{Monthly Tax} = \frac{2450}{12} \approx 204.17.
$$

Now, we calculate the monthly hazard insurance payment. The insurance premium is \$256 semiannually, so the annual premium is

$$
\text{Annual Insurance} = 256 \times 2 = 512,
$$

and the monthly insurance cost is

$$
\text{Monthly Insurance} = \frac{512}{12} \approx 42.67.
$$

The total monthly PITI (Principal, Interest, Taxes, and Insurance) payment is the sum of these three amounts:

$$
\text{Monthly PITI} \approx 452.47 + 204.17 + 42.67 \approx 699.31.
$$

This value is very close to option (a) $$ \$699.51 $$.
The monthly PITI payment is approximately \$699.51.

You purchase a home for at for 30 years. The property taxes are per year, and the hazard insurance premium is semiannually.
Find the monthly PITI payment.
Select one:
a.
b.
c.
d.

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You purchase a home for at for 30 years. The property taxes are per year, and the hazard insurance premium is semiannually. Find the monthly PITI payment. Select one: a. b. c. d.