Suppose you receive $100 at the end of each year for the next three years. If the interest rate is 7%, what is the present value of these cash flows?

To find the present value (PV) of these cash flows, we need to discount each of the future cash flows back to the present using the given interest rate of 7%. The formula for the present value of a future cash flow is:

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

where:
- $ C $ is the cash flow,
- $ r $ is the interest rate,
- $ n $ is the number of periods.

Given:
- Cash flows: $100 at the end of each year for 3 years,
- Interest rate: 7% or 0.07.

Let's break this down year by year:

1. **Year 1**: 
   \[
   PV_1 = \frac{100}{(1 + 0.07)^1} = \frac{100}{1.07} \approx 93.46
   \]

2. **Year 2**:
   \[
   PV_2 = \frac{100}{(1 + 0.07)^2} = \frac{100}{(1.07)^2} \approx \frac{100}{1.1449} \approx 87.34
   \]

3. **Year 3**:
   \[
   PV_3 = \frac{100}{(1 + 0.07)^3} = \frac{100}{(1.07)^3} \approx \frac{100}{1.225043} \approx 81.63
   \]

Now, sum these present values to find the total present value of the cash flows:

\[
PV = PV_1 + PV_2 + PV_3 \approx 93.46 + 87.34 + 81.63 = 262.43
\]

Therefore, the present value of receiving $100 at the end of each year for the next three years at an interest rate of 7% is approximately **$262.43**.

Would you like more details or have any questions?

### Related Questions:
1. How does changing the interest rate affect the present value of future cash flows?
2. What is the future value of these cash flows at the end of the third year?
3. How would the present value change if the payments were made at the beginning of each year?
4. What is the present value if the payments were to continue indefinitely (perpetuity)?
5. How does the present value change if the payments are made semi-annually instead of annually?

### Tip:
When calculating present value for multiple cash flows, it's helpful to use the formula for the present value of an annuity if the cash flows are equal and occur at regular intervals.

Calculate the present value of receiving $100 at the end of each year for 3 years at a 7% interest rate. This detailed solution demonstrates how to discount future cash flows using the time value of money formula. Suitable for Grades 10-12 and higher.

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