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 break it down into two parts:

1. **Calculate the monthly payment** that Olivia will make over the first 5 years based on a 30-year conventional mortgage at an annual interest rate of 3%, compounded monthly.
   
2. **Determine the remaining balance** (balloon payment) at the end of the 5 years.

### Step 1: Monthly Payment Calculation

The monthly payment for a fixed-rate mortgage is calculated using the following formula:

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

Where:
- $ M $ is the monthly payment.
- $ P $ is the principal loan amount ($250,000 in this case).
- $ r $ is the monthly interest rate, which is the annual interest rate divided by 12. So, $ r = \frac{3\%}{12} = \frac{0.03}{12} = 0.0025 $.
- $ n $ is the total number of payments over the 30-year period, which is $ 30 \times 12 = 360 $ months.

### Step 2: Balloon Payment Calculation

After 5 years, Olivia will have made $ 5 \times 12 = 60 $ monthly payments. The balloon payment is the remaining balance of the loan at that point, which can be calculated using the formula:

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

Where:
- $ B $ is the balance after 60 payments.
- $ P $, $ r $, and $ M $ are as defined above.
- $ n $ is now the remaining number of payments, which is $ 360 - 60 = 300 $ months.

I'll now calculate both the monthly payment and the balloon payment.The results are as follows:

- **Monthly payment** for the first 5 years: \$1,054.01
- **Balloon payment** at the end of 5 years: \$222,265.91

Would you like more details, or have any other questions? Here are 5 related questions to consider:

1. What if the interest rate was higher or lower? How would that affect the monthly payment?
2. How would the balloon payment change if Olivia made additional payments during the 5 years?
3. What are the advantages and disadvantages of choosing a balloon mortgage over a conventional one?
4. How much interest will Olivia have paid by the end of the 5-year period?
5. What happens if Olivia can't make the balloon payment at the end of 5 years?

**Tip:** If you're considering a balloon mortgage, ensure that you have a clear plan to either refinance or pay off the balance when the balloon payment is due.

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 5-year balloon mortgage of $250,000 with a 3% interest rate compounded monthly. This solution uses the amortization formula and compound interest theorem. Suitable for Grades 11-12 and college students.

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