Suppose you borrowed $250 for two years, at 8%. What is the present value of
interests and principal payments? (use r = 8% this time, as this is competitive rate).

To find the **present value** of interest and principal payments on a loan, we will discount these future payments to their value today using the formula for the present value of a lump sum:

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

Where:
- $PV$ is the present value,
- $FV$ is the future value (the loan principal and interest),
- $r$ is the interest rate (8% = 0.08), and
- $t$ is the time in years (in this case, 2 years).

Since you borrowed $250 at 8% for 2 years, we first calculate the **future value** (the total amount that you will owe, including interest):

### Step 1: Find the Future Value (Total Payments)
The total future value (FV) includes the principal plus interest. This can be calculated as:

\[
FV = P \times (1 + r)^t
\]

Where $P = 250$, $r = 0.08$, and $t = 2$.

\[
FV = 250 \times (1 + 0.08)^2
\]

Let me calculate the exact future value.The **future value** (total amount due including interest) after 2 years is **$291.60**.

### Step 2: Calculate the Present Value of Payments
Now, we will calculate the present value of this future payment using the formula:

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

Let me compute the present value of this future payment.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can easily compute the present value using the following formula:

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

Given:
- $FV = 291.60$
- $r = 0.08$
- $t = 2$

You can plug in these values to find the present value.

Would you like further details or help with this? Also, here are some related questions:

1. How is the future value of an investment calculated?
2. What happens if you change the interest rate or the loan duration?
3. How can you calculate the present value of monthly payments?
4. What is the difference between simple and compound interest?
5. How does the present value formula change for continuous compounding?

**Tip**: Always ensure to adjust your interest rate to the corresponding period if payments are not made yearly (e.g., monthly or quarterly payments).

Suppose you borrowed $250 for two years, at 8%. What is the present value of interests and principal payments? (use r = 8% this time, as this is competitive rate).

Discover how to calculate the present value of loan payments with an 8% interest rate for a $250 loan over 2 years. This problem introduces key concepts like present and future value, compound interest, and the time value of money. Suitable for high school students in Grades 10-12.

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