Olivia plans to secure a 5-year balloon mortgage of $270,000 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 4%/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. **Monthly Payment Calculation:**
   The monthly payment is based on a 30-year mortgage with a 4% annual interest rate compounded monthly. However, the mortgage will be paid for only 5 years before a balloon payment is due.

   The formula for calculating the monthly payment $ M $ for a fixed-rate mortgage is:

   \[
   M = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1}
   \]
   where:
   - $ P $ is the loan amount ($270,000),
   - $ r $ is the monthly interest rate (which is the annual interest rate divided by 12),
   - $ n $ is the total number of payments (for a 30-year mortgage, this would be $ 30 \times 12 = 360 $).

2. **Balloon Payment Calculation:**
   After 5 years (60 payments), Olivia needs to pay off the remaining balance of the mortgage. The remaining balance after $ t $ months can be calculated with:

   \[
   B = P \times \frac{(1 + r)^n - (1 + r)^t}{(1 + r)^n - 1}
   \]
   where $ t $ is the number of payments made (in this case, 60).

### Step 1: Calculate Monthly Payment $ M $

We know the following:
- Loan amount $ P = 270,000 $,
- Annual interest rate = 4% → monthly interest rate $ r = \frac{0.04}{12} $,
- Total number of payments $ n = 360 $ (for 30 years).

Now, we can calculate the monthly payment $ M $.

### Step 2: Calculate Balloon Payment $ B $

Once we know the monthly payment, we will calculate the remaining balance after 60 months (5 years). Now let’s calculate both values.The monthly payment for the first 5 years will be approximately **$1,289.02**, and the balloon payment at the end of 5 years will be approximately **$244,208.29**.

Do you have any questions or would you like further details? Here are five related questions for further exploration:

1. How does the balloon payment compare to the total amount of interest paid over 5 years?
2. What happens if the interest rate changes after 5 years?
3. How would the monthly payment change if the loan term were shorter than 30 years?
4. What is the total amount paid over the first 5 years, including interest?
5. How much could Olivia save if she made extra payments towards the principal during the first 5 years?

**Tip:** Always consider the total cost of the mortgage, including interest, before committing to a balloon mortgage, as large payments may be due at the end!

Olivia plans to secure a 5-year balloon mortgage of $270,000 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 4%/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.)

Discover how to calculate the monthly payments and balloon payment for a $270,000 5-year balloon mortgage, based on a 30-year loan at 4% interest compounded monthly. Get step-by-step details on the formulas and process involved.

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