Frank Cronin must make a balloon payment ​$30 comma 00030,000 in 55 years. Find the present value of the payment if it includes annual interest of 5.75.7​% compounded semiannuallysemiannu

To find the present value of a balloon payment of $30,000 in 5 years, with an annual interest rate of 5.7% compounded semiannually, we can use the formula for present value:

\[
PV = \frac{A}{(1 + \frac{r}{n})^{nt}}
\]

Where:
- $ PV $ is the present value (what we need to find)
- $ A $ is the future value (the balloon payment), which is $30,000
- $ r $ is the annual interest rate (as a decimal), so $ r = 5.7\% = 0.057 $
- $ n $ is the number of times the interest is compounded per year, so $ n = 2 $ (since it's compounded semiannually)
- $ t $ is the number of years, which is 5

### Plugging in the values:

\[
PV = \frac{30,000}{(1 + \frac{0.057}{2})^{2 \times 5}}
\]

Let’s calculate this step-by-step.

The present value of the $30,000 balloon payment, given a 5.7% annual interest rate compounded semiannually over 5 years, is approximately **$22,650.53**.

Would you like any further details or explanations?

Here are 5 related questions to explore:
1. How would the present value change with quarterly compounding?
2. What happens to the present value if the interest rate decreases to 4%?
3. How does the compounding frequency impact the present value of the loan?
4. What is the formula for future value in compound interest scenarios?
5. How can you calculate present value for continuous compounding?

**Tip:** Compounding frequency significantly affects the accumulation of interest, which can influence both present and future values of payments.

Frank Cronin must make a balloon payment of $30,000 in 5 years. Find the present value of the payment if it includes annual interest of 5.7% compounded semiannually.

Calculate the present value of a $30,000 balloon payment over 5 years with an interest rate of 5.7%, compounded semiannually. This detailed step-by-step guide explains how to apply the present value formula to solve for the payment, suitable for high school students studying compound interest.

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