your uncle will sell you his bicycle shop for $255,000 at a 6% nominal annual rate. The terms of the loan would require you to make 12 equal end of month payments per year for four years and then make it additional final balloon payment of $50,000 at the end of the last month what would your equal monthly payments be?

We can calculate the equal monthly payments for this loan using the **amortization formula**. The formula for monthly payments $ P $ is given by:

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

Where:
- $ P $ is the monthly payment,
- $ r $ is the monthly interest rate,
- $ PV $ is the present value of the loan (the amount being financed),
- $ n $ is the total number of payments (months).

### Known values:
- $ PV = 255,000 - 50,000 = 205,000 $ (since a balloon payment of $50,000 is due at the end, we subtract it from the total loan amount),
- Nominal annual interest rate = 6%, so the monthly interest rate is $ r = \frac{6\%}{12} = 0.005 $,
- Loan period = 4 years, so $ n = 12 \times 4 = 48 $ months.

Now, let’s calculate the monthly payment $ P $.The equal monthly payments you would need to make are approximately **$4,814.43**.

Would you like further details on the calculation or have any additional questions?

Here are 5 related questions you might consider:
1. What is the total amount paid over the life of the loan, including the balloon payment?
2. How does the balloon payment impact the overall loan structure?
3. What would the monthly payments be if the loan term were extended to 5 years?
4. How would a different interest rate (e.g., 5%) affect the monthly payments?
5. What happens to the loan if you make additional payments towards the principal?

**Tip:** Always ensure you understand the terms of a loan, including interest rates and balloon payments, as they significantly affect the total cost of borrowing.

Your uncle will sell you his bicycle shop for $255,000 at a 6% nominal annual rate. The terms of the loan would require you to make 12 equal end of month payments per year for four years and then make an additional final balloon payment of $50,000 at the end of the last month. What would your equal monthly payments be?

Find out how to calculate equal monthly payments for a $255,000 loan at a 6% interest rate, with a $50,000 balloon payment. This detailed guide explains the loan amortization formula and the effect of balloon payments, making it ideal for students of financial mathematics.

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