Olivia plans to secure a 5-year balloon mortgage of $250,000 toward the purchase of a condominium. Her monthly payment for the 5 years is calculated on the basis of a 30-year conventional mortgage at the rate of 3%/year compounded monthly. At the end of the 5 years, Olivia is required to pay the balance owed (the "balloon" payment). What will be her monthly payment for the first 5 years, and what will be her balloon payment? (Round your answers to the nearest cent.)


monthly payment    

$ 

balloon payment    

$ 

To solve this problem, we need to calculate two things:

1. **Monthly payment** for the first 5 years, based on a 30-year mortgage with a 3% annual interest rate, compounded monthly.
2. **Balloon payment** after 5 years, which is the remaining balance on the mortgage.

### Step 1: Monthly Payment Calculation

The formula for the monthly payment $ M $ of a mortgage is given by:

\[
M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}
\]

Where:
- $ P = 250,000 $ (principal loan amount),
- $ r = \frac{0.03}{12} = 0.0025 $ (monthly interest rate, since 3% is compounded monthly),
- $ n = 30 \times 12 = 360 $ (total number of payments for a 30-year mortgage).

### Step 2: Balloon Payment Calculation

The balloon payment is the remaining balance after 5 years. We use the formula for the remaining balance $ B $ at time $ t $:

\[
B = P \times \frac{(1 + r)^n - (1 + r)^t}{(1 + r)^n - 1}
\]

Where:
- $ t = 5 \times 12 = 60 $ (total number of payments made after 5 years).

Let's calculate the monthly payment and balloon payment.### Results:
- **Monthly payment for the first 5 years:** \$1,054.01
- **Balloon payment at the end of 5 years:** \$222,265.91

These values are rounded to the nearest cent.

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Olivia plans to secure a 5-year balloon mortgage of $250,000 toward the purchase of a condominium. Her monthly payment for the 5 years is calculated on the basis of a 30-year conventional mortgage at the rate of 3%/year compounded monthly. At the end of the 5 years, Olivia is required to pay the balance owed (the 'balloon' payment). What will be her monthly payment for the first 5 years, and what will be her balloon payment? (Round your answers to the nearest cent.)

Learn how to calculate the monthly payment and balloon payment for a $250,000 balloon mortgage over 5 years with an interest rate of 3% compounded monthly. This guide covers mortgage amortization and interest compounding concepts, with detailed formulas and step-by-step solutions.

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