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 $ given a future amount $ A $, interest rate $ r $, and time $ t $, we use the formula for present value with compound interest:

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

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

### Step 1: Substitute the values

\[
P = \frac{35000}{\left(1 + \frac{0.12}{4}\right)^{4 \times 14}}
\]

### Step 2: Simplify inside the parentheses

\[
P = \frac{35000}{\left(1 + 0.03\right)^{56}}
\]
\[
P = \frac{35000}{(1.03)^{56}}
\]

### Step 3: Calculate $ (1.03)^{56} $

\[
(1.03)^{56} \approx 5.268
\]

### Step 4: Divide to find $ P $

\[
P = \frac{35000}{5.268} \approx 6645.23
\]

### Answer
The present value is approximately **$6,645.23**.

Would you like more details or have any questions?

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### Related Questions
1. How would the present value change if the interest rate were 10% instead of 12%?
2. What would the present value be if the compounding frequency was annual instead of quarterly?
3. How does the formula change if compounding is done monthly?
4. How much would need to be invested today to reach $50,000 in 10 years at the same interest rate?
5. How does the present value calculation differ if the interest rate is continuously compounded?

#### Tip
When dealing with compound interest, higher compounding frequencies (quarterly, monthly) result in a slightly lower present value due to more frequent application of interest.

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 a 12% interest rate compounded quarterly for 14 years. This solution includes a detailed step-by-step approach using the compound interest formula, making it suitable for Grades 11-12 finance and mathematics studies.

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