You are to receive $4,900, $5,500 and $7,400 at the end of each of the next 3 years. If the market interest rate is 5.40%, how much would this payment stream be worth today?

To determine the present value (worth today) of the given payment stream, we need to discount each payment back to the present using the market interest rate of 5.40%. This involves using the Present Value (PV) formula:

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

Where:
- $C$ is the cash flow (the payment),
- $r$ is the interest rate (expressed as a decimal),
- $n$ is the number of years until the payment is received.

We will discount each payment separately and then sum the present values to find the total worth of the payment stream today.

Given:
- $C_1 = 4,900$, $n_1 = 1$ year,
- $C_2 = 5,500$, $n_2 = 2$ years,
- $C_3 = 7,400$, $n_3 = 3$ years,
- $r = 0.054$ (5.40%).

### Step 1: Calculate the present value of each payment.
For the payment at the end of year 1:

\[
PV_1 = \frac{4,900}{(1 + 0.054)^1}
\]

For the payment at the end of year 2:

\[
PV_2 = \frac{5,500}{(1 + 0.054)^2}
\]

For the payment at the end of year 3:

\[
PV_3 = \frac{7,400}{(1 + 0.054)^3}
\]

### Step 2: Add the present values to get the total present value.

Let's calculate it step by step.The present value of each payment is as follows:
- Year 1 payment of $4,900: Present value = \$4,648.96
- Year 2 payment of $5,500: Present value = \$4,950.87
- Year 3 payment of $7,400: Present value = \$6,319.90

### Total present value (worth today): \$15,919.72

Would you like more details or have any questions?

Here are 5 related questions you might explore:
1. How would the total present value change if the interest rate increased to 6%?
2. What if the payments were received quarterly instead of annually?
3. How would a delay of 1 year in all payments affect the present value?
4. Can we apply this same method to continuous cash flows?
5. How does a varying interest rate over the years influence the calculation?

**Tip:** The higher the interest rate, the lower the present value of future cash flows.

Find out how to calculate the present value of a payment stream of $4,900, $5,500, and $7,400 to be received over the next 3 years at an interest rate of 5.40%. Learn key concepts like discounting cash flows and the time value of money. This is suitable for college-level finance or mathematics students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation