on list tion 1 stion 2 estion 3 restion 4 uestion 5 2uestion 6 The price of a condominium is $$ \$ 110,000 $$. The bank requires a $$ 5 \% $$ down payment and one point at the time of closing. The cost of the condominium is financed with a 30 -year fixed-rate mortgage at $$ 7.5 \% $$. Use the following formula to đetermine the regular payment amount. Complele parts (a) through (e) below. $$ P M T=\frac{P\left(\frac{r}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]} $$ a. Find the required down payment. $$ \$ 5,500 $$ b. Find the amount of the mortgage. $$ \$ 104,500 $$ c. How much must be paid for the one point at closing? $$ \$ 1,045 $$ (Round to the nearest dollar as needed.) d. Find the monthly payment (excluding escrowed taxes and insurance). $$ \$ $$ $$ \square $$ (Round to the nearest dollar as needed.)

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Given:
- The price of the condominium is $110,000.
- The bank requires a 5% down payment and one point at the time of closing.
- The cost of the condominium is financed with a 30-year fixed-rate mortgage at 7.5%.

We need to find the regular payment amount using the formula:
$$ P M T = \frac{P\left(\frac{r}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]} $$

Let's break down the problem into parts (a) through (e) as requested:

a. Find the required down payment:
The down payment is 5% of the price of the condominium.
$$ \text{Down payment} = 0.05 \times \$110,000 = \$5,500 $$

b. Find the amount of the mortgage:
The amount of the mortgage is the price of the condominium minus the down payment.
$$ \text{Mortgage amount} = \$110,000 - \$5,500 = \$104,500 $$

c. How much must be paid for the one point at closing:
One point is equal to 1% of the mortgage amount.
$$ \text{One point} = 0.01 \times \$104,500 = \$1,045 $$

d. Find the monthly payment (excluding escrowed taxes and insurance):
To find the monthly payment, we need to substitute the values into the formula:
$$ P M T = \frac{\$104,500\left(\frac{0.075}{12}\right)}{\left[1-\left(1+\frac{0.075}{12}\right)^{-12 \times 30}\right]} $$

Let's calculate the monthly payment.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{104500\left(\frac{0.075}{12}\right)}{1-\left(1+\frac{0.075}{12}\right)^{-12\times 30}}$$
- step1: Divide the terms:
  $$\frac{104500\left(\frac{0.075}{12}\right)}{1-\left(1+\frac{1}{160}\right)^{-12\times 30}}$$
- step2: Add the numbers:
  $$\frac{104500\left(\frac{0.075}{12}\right)}{1-\left(\frac{161}{160}\right)^{-12\times 30}}$$
- step3: Divide the terms:
  $$\frac{104500\times \frac{1}{160}}{1-\left(\frac{161}{160}\right)^{-12\times 30}}$$
- step4: Multiply the numbers:
  $$\frac{104500\times \frac{1}{160}}{1-\left(\frac{161}{160}\right)^{-360}}$$
- step5: Multiply the numbers:
  $$\frac{\frac{5225}{8}}{1-\left(\frac{161}{160}\right)^{-360}}$$
- step6: Subtract the numbers:
  $$\frac{\frac{5225}{8}}{\frac{161^{360}-160^{360}}{161^{360}}}$$
- step7: Multiply by the reciprocal:
  $$\frac{5225}{8}\times \frac{161^{360}}{161^{360}-160^{360}}$$
- step8: Multiply the fractions:
  $$\frac{5225\times 161^{360}}{8\left(161^{360}-160^{360}\right)}$$
- step9: Multiply:
  $$\frac{5225\times 161^{360}}{8\times 161^{360}-8\times 160^{360}}$$
The monthly payment (excluding escrowed taxes and insurance) is approximately $730.68.
a. Down payment: \$5,500 b. Mortgage amount: \$104,500 c. Cost of one point: \$1,045 d. Monthly payment: \$731

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