A payment of $940 scheduled to be paid today and a second payment of $1,230 to be paid in six months from today are to be replaced by a single equivalent payment.

What total payment made today would place the payee in the same financial position as the scheduled payments if money can earn 21/4%? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

To find the single equivalent payment made today that would place the payee in the same financial position, we need to discount both payments using the given interest rate. The formula for discounting a future payment to its present value (PV) is:

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

Where:
- $FV$ is the future value (the amount to be paid),
- $i$ is the interest rate per period,
- $t$ is the time in periods (years, months, etc.).

### Step 1: Discount the first payment of $940 made today
Since this payment is made today, the present value is simply the amount itself:

\[
PV_1 = 940
\]

### Step 2: Discount the second payment of $1,230 due in 6 months
The interest rate is $ 2.25\% $ annually, which is $ \frac{21}{4} \%$, or $0.0225$ as a decimal. Since the payment is due in 6 months (or 0.5 years), the present value is:

\[
PV_2 = \frac{1,230}{(1 + 0.0225)^{0.5}}
\]

### Step 3: Find the total equivalent payment today
The total equivalent payment today is the sum of the present values of the two payments:

\[
PV_{\text{total}} = PV_1 + PV_2
\]

I'll now calculate the total present value.The total equivalent payment that should be made today to place the payee in the same financial position is approximately **$2,156.39**.

Would you like any further details on how this was calculated or have any questions?

Here are 5 related questions to explore further:
1. How would the total payment change if the interest rate was higher, say 5%?
2. What would happen if the second payment was made in one year instead of six months?
3. How do changes in the timing of payments affect their present value?
4. How is the formula for discounting payments derived from the concept of compound interest?
5. Could we apply a similar method for multiple future payments?

**Tip:** The longer a payment is delayed, the lower its present value, especially with higher interest rates.

A payment of $940 scheduled to be paid today and a second payment of $1,230 to be paid in six months from today are to be replaced by a single equivalent payment. What total payment made today would place the payee in the same financial position as the scheduled payments if money can earn 2.25%? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Find out how to calculate the total present value of two payments of $940 today and $1,230 in 6 months, using a 2.25% annual interest rate. This example applies the present value formula and explains discounting future payments to their equivalent value today. Suitable for advanced high school students or introductory finance courses.

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