Calculate the present value. (Round your answer to two decimal places.)

*A* = $35,000, *r* = 12% compounded quarterly, *t* = 14 years

$ 

To calculate the present value ($ P $) of an amount $ A $ compounded quarterly, we use the formula:

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

where:
- $ A = 35,000 $ (the future amount),
- $ r = 0.12 $ (annual interest rate of 12%),
- $ n = 4 $ (since the interest is compounded quarterly),
- $ t = 14 $ years.

### Step-by-Step Solution:

1. **Calculate the quarterly rate**:
   \[
   \frac{r}{n} = \frac{0.12}{4} = 0.03
   \]

2. **Calculate the total number of compounding periods**:
   \[
   nt = 4 \times 14 = 56
   \]

3. **Calculate the present value**:
   \[
   P = \frac{35,000}{\left(1 + 0.03\right)^{56}}
   \]

4. **Solve the exponent and division**:
   \[
   P = \frac{35,000}{(1.03)^{56}}
   \]

Using a calculator to find $(1.03)^{56}$:

\[
(1.03)^{56} \approx 5.4591
\]

5. **Final Calculation**:
   \[
   P \approx \frac{35,000}{5.4591} \approx 6413.83
   \]

### Answer:
The present value $ P $ is approximately **$6,413.83**.

Would you like more details or have any questions?

---

1. How does the compounding frequency affect the present value?
2. What would the present value be if compounded monthly instead?
3. How does increasing the rate to 15% impact the present value?
4. Can you apply the formula to find future value given present value?
5. How does a longer time period affect the present value?

**Tip**: When compounding more frequently, the effective interest rate increases, decreasing the present value.

Calculate the present value. (Round your answer to two decimal places.)

*A* = $35,000, *r* = 12% compounded quarterly, *t* = 14 years

Learn how to calculate the present value of $35,000 with an interest rate of 12% compounded quarterly over 14 years. This detailed solution covers compound interest concepts, exponential calculations, and provides a step-by-step breakdown. Ideal for high school students or anyone studying finance.

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