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PMT \( =\frac{\mathrm{P}\left(\frac{r}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]} \) The price of a condominium is \( \$ 110,000 \). The bank requires a \( 5 \% \) down payment and one point at the time of closing. determine the regular payment amount. Complete parts (a) through (e) below. \[ \begin{array}{l}\text { a. Find the required down payment. } \\ \$ 5,500 \\ \text { b. Find the amount of the mortgage. } \\ \$ \square\end{array} \]

Ask by Ruiz Olson. in the United States
Mar 14,2025

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Answer

**a. Required down payment:** \$5,500 **b. Amount of the mortgage:** \$104,500

Solution

To solve the problem step by step, we will first extract the known conditions and then proceed with the calculations. ### Known Conditions: 1. Price of the condominium \( P = 110,000 \) 2. Down payment percentage \( d = 5\% \) 3. Down payment amount \( D = P \times d \) 4. The mortgage amount will be the price minus the down payment. ### Step a: Find the required down payment. The down payment can be calculated as follows: \[ D = P \times d = 110,000 \times 0.05 \] Now, let's calculate the down payment. ### Step b: Find the amount of the mortgage. The mortgage amount \( M \) can be calculated using the formula: \[ M = P - D \] Now, let's perform the calculations for both parts (a) and (b). I'll calculate the down payment and the mortgage amount. Calculate the value by following steps: - step0: Calculate: \(110000-\left(110000\times 0.05\right)\) - step1: Multiply the numbers: \(110000-5500\) - step2: Subtract the numbers: \(104500\) Calculate or simplify the expression \( 110000 * 0.05 \). Calculate the value by following steps: - step0: Calculate: \(110000\times 0.05\) - step1: Multiply the numbers: \(5500\) ### Step a: Find the required down payment. The required down payment is: \[ D = 5,500 \] ### Step b: Find the amount of the mortgage. The amount of the mortgage is: \[ M = 104,500 \] ### Summary of Results: - **a. Required down payment:** \( \$ 5,500 \) - **b. Amount of the mortgage:** \( \$ 104,500 \) Now, if you would like to proceed with parts (c) through (e), please provide the necessary details such as the interest rate, the number of payments per year, and the total number of years for the mortgage.

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To determine the amount of the mortgage, we first need to subtract the down payment from the price of the condominium. Since the down payment is \( \$5,500 \), we calculate the mortgage amount as follows: \[ \text{Mortgage Amount} = \text{Price of Condominium} - \text{Down Payment} \] \[ \text{Mortgage Amount} = \$110,000 - \$5,500 = \$104,500 \] Now you have \( \$104,500 \) as the mortgage amount. Additionally, let’s dive into some relevant factors that can make your mortgage journey smoother: Mortgage payments can fluctuate based on interest rates, term lengths, and specific lending conditions. Remember that securing a loan at a lower interest rate can reduce your monthly payments significantly, allowing you to save thousands in the long run! Also, avoid common pitfalls like not calculating your total monthly expenses including taxes, insurance, and potential homeowners association fees. This will help you maintain financial flexibility and avoid surprises when the bills start rolling in!

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