Calculate the equivalent value of the payment on the rescheduled date. Use the rescheduled payment date as the focal date.

Round your answer to two decimal places, no units necessary.

$7,740 due 2 years ago, rescheduled to 22 months from now at 3.9% p.a

To calculate the equivalent value of a payment rescheduled to a new date using the new date as the focal date, we must account for interest, adjusting the original amount based on how far the original payment date is from the focal point.

### Given:
- Original payment: $7,740 due 2 years ago.
- Rescheduled to: 22 months from now.
- Interest rate: 3.9% per annum.

We need to calculate the equivalent value of the original payment at the rescheduled date, using the rescheduled date as the focal point.

#### Step 1: Calculate the total time difference in years.
- The original payment was due **2 years ago**, and the new payment date is **22 months from now**.
- The total time between the original due date and the rescheduled date is:
  \[
  2 + \frac{22}{12} = 2 + 1.8333 = 3.8333 \text{ years}.
  \]
This is the period for which we need to adjust the payment.

#### Step 2: Adjust the payment using the interest rate.
The formula for adjusting the payment to a new focal date based on simple interest is:
\[
\text{Future Value (FV)} = \text{Present Value (PV)} \times (1 + rt),
\]
where:
- $PV = 7,740$ (the original amount),
- $r = 3.9\%$ per annum (expressed as 0.039),
- $t = 3.8333$ years (the time difference).

Substituting the values:
\[
FV = 7,740 \times (1 + 0.039 \times 3.8333).
\]

#### Step 3: Perform the calculation.
\[
FV = 7,740 \times (1 + 0.1495) = 7,740 \times 1.1495 = 8,899.23.
\]

The equivalent value of the payment on the rescheduled date is **8,899.23**.

Would you like any further explanation or details?

Here are 5 related questions:
1. How is compound interest applied in similar problems?
2. How would the equivalent value change with a higher interest rate?
3. What if the payment date was rescheduled to a past date?
4. How does the formula change if the interest rate is compounded monthly?
5. What is the difference between simple interest and compound interest?

**Tip:** Always ensure the time is in the same units (years, months) when calculating interest.

Calculate the equivalent value of the payment on the rescheduled date. Use the rescheduled payment date as the focal date. Round your answer to two decimal places, no units necessary. $7,740 due 2 years ago, rescheduled to 22 months from now at 3.9% p.a.

Learn how to calculate the future value of a payment of $7,740 due 2 years ago, rescheduled to 22 months from now at an interest rate of 3.9% per annum. This step-by-step guide covers simple interest and time value of money. Suitable for students in Grades 10-12.

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