Olivia plans to secure a 5-year balloon mortgage of $240,000 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?

To solve this problem, we need to determine two things:
1. **The monthly mortgage payment for the first 5 years.**
2. **The balloon payment at the end of 5 years.**

### Step 1: Monthly Payment for the First 5 Years

Olivia's monthly payment is calculated based on a 30-year conventional mortgage at an annual interest rate of 4%, compounded monthly. The loan amount is $240,000. The formula to calculate the monthly payment (M) for a fixed-rate mortgage is given by:

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

Where:
- $P$ = loan amount = $240,000
- $r$ = monthly interest rate = $\frac{4\%}{12} = \frac{0.04}{12} = 0.0033333$
- $n$ = total number of monthly payments for a 30-year mortgage = 30 years $\times$ 12 months/year = 360 months

Substituting the values:

\[
M = 240,000 \cdot \frac{0.0033333(1 + 0.0033333)^{360}}{(1 + 0.0033333)^{360} - 1}
\]

I'll calculate this value.

### Step 2: Balloon Payment at the End of 5 Years

After 5 years (60 months), Olivia will owe the remaining balance on the loan, which is called the "balloon payment." To find the balloon payment, we use the mortgage balance formula:

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

Where:
- $P$ = loan amount = $240,000
- $r$ = monthly interest rate = 0.0033333
- $n$ = total number of payments (360 months)
- $t$ = number of months paid (60 months)

I'll calculate this as well.### Results:
1. **Monthly payment for the first 5 years**: \$1,145.80 (rounded to two decimal places).
2. **Balloon payment at the end of 5 years**: \$217,074.03 (rounded to two decimal places).

Let me know if you'd like more details or have any questions. 

Here are 5 follow-up questions that could help you explore the topic further:
1. What would the monthly payment be if the interest rate were 5% instead of 4%?
2. How would the balloon payment change if Olivia paid off the loan over 10 years instead of 5?
3. How much total interest does Olivia pay over the 5 years?
4. What happens to the loan if Olivia refinances the mortgage at the end of 5 years?
5. How would the monthly payment change if the mortgage term was 15 years instead of 30 years?

**Tip**: You can reduce the balloon payment by making extra payments towards the principal during the first 5 years!

Olivia plans to secure a 5-year balloon mortgage of $240,000 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?

Find out how to calculate the monthly mortgage payment for Olivia's 5-year balloon mortgage of $240,000, based on a 30-year mortgage at 4% interest. This detailed solution covers loan amortization, compound interest, and the balloon payment at the end of 5 years. Ideal for students in financial mathematics or business studies.

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