The price of a condominium is $$ \$ 121,000 $$. 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 $$ 6.5 \% $$. Use the following formula to , determine the regular payment amount. Complete parts (a) through (e) below. PMT $$ =\frac{\mathrm{P}\left(\frac{\mathrm{r}}{\mathrm{n}}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]} $$

Question

UpStudy AI · Accepted Answer

To determine the regular payment amount for the condominium, we will follow the steps outlined in the problem. Let's break it down step by step.

### Given Information:
- Price of the condominium, $$ P = 121,000 $$
- Down payment percentage = $$ 5\% $$
- Interest rate = $$ 6.5\% $$ (annual)
- Loan term = $$ 30 $$ years
- Points at closing = $$ 1 $$ point (1% of the loan amount)

### Step 1: Calculate the Down Payment
The down payment is calculated as follows:
$$
\text{Down Payment} = P \times \text{Down Payment Percentage} = 121,000 \times 0.05 = 6,050
$$

### Step 2: Calculate the Loan Amount
The loan amount is the price of the condominium minus the down payment:
$$
\text{Loan Amount} = P - \text{Down Payment} = 121,000 - 6,050 = 114,950
$$

### Step 3: Calculate the Monthly Interest Rate and Number of Payments
- Annual interest rate $$ r = 6.5\% = 0.065 $$
- Monthly interest rate $$ \frac{r}{n} = \frac{0.065}{12} $$
- Number of payments $$ n \times t = 12 \times 30 = 360 $$

Calculating the monthly interest rate:
$$
\frac{r}{n} = \frac{0.065}{12} \approx 0.00541667
$$

### Step 4: Substitute Values into the Payment Formula
The formula for the monthly payment $$ PMT $$ is:
$$
PMT = \frac{P \left( \frac{r}{n} \right)}{1 - \left( 1 + \frac{r}{n} \right)^{-nt}}
$$
Substituting the values:
- $$ P = 114,950 $$
- $$ \frac{r}{n} \approx 0.00541667 $$
- $$ nt = 360 $$

Calculating $$ PMT $$:
$$
PMT = \frac{114,950 \times 0.00541667}{1 - \left(1 + 0.00541667\right)^{-360}}
$$

Calculating $$ \left(1 + 0.00541667\right)^{-360} $$:
$$
1 + 0.00541667 \approx 1.00541667
$$
$$
(1.00541667)^{-360} \approx 0.174110
$$

Now substituting back into the formula:
$$
PMT = \frac{114,950 \times 0.00541667}{1 - 0.174110}
$$
$$
PMT = \frac{623.75}{0.825890} \approx 754.06
$$

### Final Result
The regular monthly payment amount is approximately:
$$
\boxed{754.06}
$$

### Additional Parts (if applicable)
If there are additional parts (like calculating total payments, total interest paid, etc.), please specify, and I can assist with those calculations as well.
The regular monthly payment for the condominium is approximately \$754.06.

The price of a condominium is . The bank requires a 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 . Use the following formula to ,
determine the regular payment amount. Complete parts (a) through (e) below.
PMT

Upstudy AI Solution

Answer

Solution

Given Information:

Step 1: Calculate the Down Payment

Step 2: Calculate the Loan Amount

Step 3: Calculate the Monthly Interest Rate and Number of Payments

Step 4: Substitute Values into the Payment Formula

Final Result

Additional Parts (if applicable)

Bonus Knowledge

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The price of a condominium is . The bank requires a 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 . Use the following formula to , determine the regular payment amount. Complete parts (a) through (e) below. PMT