Questions: The price of a condominium is 125,000. 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 10%. Use the following formula to determine the regular payment amount. Complete parts (a) through (e) below. PMT = P(r/n) / [1 - (1 + r/n)^(-nt)] a. Find the required down payment. 6250 b. Find the amount of the mortgage. 118,750 c. How much must be paid for the one point at closing? (Round to the nearest dollar as needed.)

The price of a condominium is 125,000. 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 10%. Use the following formula to determine the regular payment amount. Complete parts (a) through (e) below.

PMT = P(r/n) / [1 - (1 + r/n)^(-nt)]

a. Find the required down payment.
6250
b. Find the amount of the mortgage.
118,750
c. How much must be paid for the one point at closing?
(Round to the nearest dollar as needed.)

Transcript text: The price of a condominium is $\$ 125,000$. 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 $10 \%$. Use the following formula to determine the regular payment amount. Complete 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. \$ 6250 b. Find the amount of the mortgage. \$ 118,750 c. How much must be paid for the one point at closing? \$ (Round to the nearest dollar as needed.)

Solution

Solution Steps

Step 1: Calculate the required down payment

The required down payment is calculated as $C \times d = 125000 \times 0.05 = 6250$.

Step 2: Calculate the amount of the mortgage

The amount of the mortgage is calculated as $C - $ down payment $= 125000 - 6250 = 118750$.

Step 3: Calculate the cost of points at closing

The cost of points at closing is calculated as $p \times$ amount of the mortgage $= 0.01 \times 118750 = 1188$.

Step 4: Calculate the monthly payment amount

Using the formula: \[PMT = \frac{P\left(\frac{r}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-nt}\right]}\] where $P = 118750, r = 0.1, n = 12, t = 30$, the monthly payment amount is $PMT = 1042$.

Step 5: Calculate the total cost of interest over the term of the mortgage

The total cost of interest over the term of the mortgage is calculated as $PMT \times nt - P = 1042 \times 360 - 118750 = 256412$.

Final Answer:

The required down payment is 6250, the amount of the mortgage is 118750, the cost of points at closing is 1188, the monthly payment amount is 1042, and the total cost of interest over the term of the mortgage is 256412.

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