You need a 30-year, fixed-rate mortgage to buy a new home for $270,000. Your mortgage bank will lend you the money at an APR of 5.1 percent for this 360-month loan. However, you can afford monthly payments of only $1,000, so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment.

How large will this balloon payment have to be for you to keep your monthly payments at $1,000?

To find the balloon payment required for the given mortgage conditions, we need to calculate the remaining balance after making 360 payments of $1,000 each.

### Step 1: Calculate the monthly interest rate
The annual percentage rate (APR) is 5.1%. To find the monthly interest rate:

\[
r = \frac{5.1\%}{12} = \frac{0.051}{12} \approx 0.00425
\]

### Step 2: Calculate the present value of the monthly payments
The loan balance that $1,000 per month can amortize over 360 months can be calculated using the present value of an annuity formula:

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

Where:
- $P$ is the monthly payment, $P = 1,000$
- $r$ is the monthly interest rate, $r = 0.00425$
- $n$ is the number of payments, $n = 360$

\[
PV = 1,000 \times \frac{1 - (1 + 0.00425)^{-360}}{0.00425}
\]

### Step 3: Calculate the present value
Now, let's compute the present value:

\[
PV = 1,000 \times \frac{1 - (1.00425)^{-360}}{0.00425}
\]

\[
PV \approx 1,000 \times \frac{1 - 0.23657}{0.00425} \approx 1,000 \times 179.2435 \approx 179,243.50
\]

### Step 4: Calculate the balloon payment
The total loan amount is $270,000. The amount amortized by the monthly payments is $179,243.50. The remaining balance, which will be the balloon payment, is:

\[
\text{Balloon Payment} = 270,000 - 179,243.50 = 90,756.50
\]

### Conclusion
The balloon payment at the end of the loan will have to be **$90,756.50** for you to keep your monthly payments at $1,000.

Would you like more details or have any questions?

Here are 5 related questions you might find useful:

1. How does the balloon payment affect the total interest paid over the loan term?
2. What would be the monthly payment if the balloon payment were not allowed?
3. How would the balloon payment change if the interest rate was different?
4. What are the risks associated with choosing a balloon payment?
5. How does the length of the loan affect the balloon payment?

**Tip:** When considering a mortgage with a balloon payment, it's crucial to plan ahead for the large final payment to avoid financial strain.

You need a 30-year, fixed-rate mortgage to buy a new home for $270,000. Your mortgage bank will lend you the money at an APR of 5.1 percent for this 360-month loan. However, you can afford monthly payments of only $1,000, so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment. How large will this balloon payment have to be for you to keep your monthly payments at $1,000?

Find out how to calculate the balloon payment needed to keep your monthly payments at $1,000 for a $270,000, 30-year fixed-rate mortgage with a 5.1% APR. Learn about loan amortization and the present value of annuities in this step-by-step guide.

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