An investment will pay you $89,000 in four years. Assume the appropriate discount rate is 8.25 percent compounded daily. What is the present value?

Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16. Use 365 days in a year.



To find the present value (PV) of an investment, we use the formula for present value with daily compounding:

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

Where:
- $FV$ is the future value, which is \$89,000.
- $r$ is the annual interest rate (8.25% or 0.0825).
- $n$ is the number of compounding periods per year (365 for daily compounding).
- $t$ is the time in years (4 years).

Now, let's plug in the values and calculate:

\[
PV = \frac{89,000}{(1 + \frac{0.0825}{365})^{365 \times 4}}
\]

I will compute this.The present value (PV) of the investment is \$63,986.60 (rounded to two decimal places).

Would you like further details on the calculation or have any questions?

Here are 5 related questions to explore:
1. How does the frequency of compounding affect the present value?
2. What would the present value be if the discount rate changed to 7%?
3. How would the present value change if the investment matured in 5 years instead of 4?
4. What if the investment was compounded monthly instead of daily?
5. How can the future value be calculated given the present value and interest rate?

**Tip:** The more frequently interest is compounded, the lower the present value for a given future amount.

An investment will pay you $89,000 in four years. Assume the appropriate discount rate is 8.25 percent compounded daily. What is the present value?

Calculate the present value of an investment worth $89,000 after four years with an interest rate of 8.25%, compounded daily. This finance problem uses the present value formula for compound interest and covers concepts such as the time value of money and exponential growth.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation