Frank Cronin must make a balloon payment ​$20 comma 000 in 5 years. Find the present value of the payment if it includes annual interest of 6.7​% compounded quarterly.
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Part 1
The present value is ​$
  

To find the present value of the balloon payment, we can use the present value formula for compound interest:

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

Where:
- $ PV $ is the present value (what we're solving for).
- $ FV $ is the future value (the balloon payment amount, $20,000).
- $ r $ is the annual interest rate (6.7% or 0.067 as a decimal).
- $ n $ is the number of times the interest is compounded per year (quarterly, so $ n = 4 $).
- $ t $ is the number of years (5 years).

### Step-by-step calculation:
1. Convert the interest rate to a decimal: $ r = 0.067 $.
2. The interest is compounded quarterly, so $ n = 4 $.
3. The time period is $ t = 5 $ years.
4. Future value $ FV = 20,000 $.

Now, we can plug these values into the formula:

\[
PV = \frac{20,000}{\left(1 + \frac{0.067}{4}\right)^{4 \times 5}}
\]

Let's calculate this value.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you'd like to continue, you can manually calculate the present value using the formula provided earlier. Here it is again:

\[
PV = \frac{20,000}{\left(1 + \frac{0.067}{4}\right)^{4 \times 5}}
\]

Let me know if you'd like further clarification on the steps!

Here are some related questions you might find helpful:
1. How does compounding frequency affect present value calculations?
2. What would the present value be with a different interest rate, like 5%?
3. How does the formula change for continuous compounding?
4. What is the difference between simple interest and compound interest?
5. How would inflation impact the value of the $20,000 balloon payment in 5 years?

**Tip:** Compounding quarterly means the interest is applied four times per year, so the effect of interest grows faster than with annual compounding.

Frank Cronin must make a balloon payment of $20,000 in 5 years. Find the present value of the payment if it includes annual interest of 6.7% compounded quarterly.

Learn how to calculate the present value of a $20,000 balloon payment due in 5 years with an annual interest rate of 6.7% compounded quarterly. This solution walks through the compound interest formula step-by-step, ideal for students in Grades 10-12.

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