Frank Cronin must make a balloon payment 

​$20 comma 00020,000 

in 

33 

years. Find the present value of the payment if it includes annual interest of 

6.16.1​% 

compounded 

quarterlyquarterly.

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Part 1

The present value is 

​$enter your response here.

​(Round to the appropriate​ cent.)

To find the present value of a balloon payment, we can use the formula for the present value of a lump sum:

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

Where:
- $ PV $ is the present value
- $ FV $ is the future value (the balloon payment), which is $20,000
- $ r $ is the annual interest rate (expressed as a decimal), which is 6.1% or 0.061
- $ n $ is the number of compounding periods per year (since it's compounded quarterly, $ n = 4 $)
- $ t $ is the number of years, which is 33 years.

Now, let’s calculate the present value:

\[
PV = \frac{20000}{(1 + \frac{0.061}{4})^{4 \times 33}}
\]

I will calculate this for you.The present value of the balloon payment is approximately **$2,712.65**.

Would you like more details or have any other questions?

Here are 5 related questions you could explore:
1. How would the present value change if the interest rate was different?
2. What happens if the compounding frequency is annually instead of quarterly?
3. How does the present value change if the payment is due in 20 years instead of 33?
4. What if the balloon payment amount was $30,000 instead of $20,000?
5. How does inflation affect the value of money over time in these scenarios?

**Tip:** When interest is compounded more frequently, the present value tends to decrease for a future payment.

Frank Cronin must make a balloon payment of $20,000 in 33 years. Find the present value of the payment if it includes annual interest of 6.1% compounded quarterly.

Learn how to calculate the present value of a $20,000 balloon payment due in 33 years with an annual interest rate of 6.1% compounded quarterly. This financial math problem demonstrates how to apply the compound interest formula to find the present value of future payments. Suitable for college-level financial mathematics.

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