What is the present value of the following? Use Appendix B as an approximate answer, but calculate your final answer using the formula and financial calculator methods.

$8,600 in 12 years at 8 percent?
Note: Do not round intermediate calculations. Round your final answer to 2 decimal places.

$20,700 in 7 years at 10 percent?
Note: Do not round intermediate calculations. Round your final answer to 2 decimal places.

$28,400 in 18 years at 6 percent?
Note: Do not round intermediate calculations. Round your final answer to 2 decimal places.

To calculate the **Present Value (PV)** of a future sum of money, you can use the **Present Value formula**:

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

Where:
- $ PV $ = Present Value
- $ FV $ = Future Value (the amount of money in the future)
- $ r $ = interest rate (as a decimal)
- $ n $ = number of periods (years)

Let's calculate the PV for each case:

### 1. **$8,600 in 12 years at 8 percent**

Given:
- $ FV = 8,600 $
- $ r = 8\% = 0.08 $
- $ n = 12 $

\[
PV = \frac{8,600}{(1 + 0.08)^{12}}
\]

### 2. **$20,700 in 7 years at 10 percent**

Given:
- $ FV = 20,700 $
- $ r = 10\% = 0.10 $
- $ n = 7 $

\[
PV = \frac{20,700}{(1 + 0.10)^{7}}
\]

### 3. **$28,400 in 18 years at 6 percent**

Given:
- $ FV = 28,400 $
- $ r = 6\% = 0.06 $
- $ n = 18 $

\[
PV = \frac{28,400}{(1 + 0.06)^{18}}
\]

I will now calculate the present values for each scenario.Here are the present values for each scenario:

1. **$8,600 in 12 years at 8 percent**:  
   Present Value = **$3,415.18**

2. **$20,700 in 7 years at 10 percent**:  
   Present Value = **$10,622.37**

3. **$28,400 in 18 years at 6 percent**:  
   Present Value = **$9,949.76**

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. How does an increase in interest rate affect the present value of a future sum?
2. What is the future value if $3,415.18 is invested for 12 years at 8%?
3. How would the present value change if the time periods were shorter?
4. What role does compound interest play in present value calculations?
5. How can present value help in making investment decisions?

**Tip**: The higher the interest rate or the longer the time, the lower the present value of a future sum.

What is the present value of the following? Use Appendix B as an approximate answer, but calculate your final answer using the formula and financial calculator methods.

$8,600 in 12 years at 8 percent?
$20,700 in 7 years at 10 percent?
$28,400 in 18 years at 6 percent?

Learn how to calculate the present value of future sums of money using the present value formula. We solve for $8,600 in 12 years at 8%, $20,700 in 7 years at 10%, and $28,400 in 18 years at 6%. Understand the effect of time and interest rates on the present value.

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