To determine the single equivalent payment that is economically equivalent to the given cash flows, we will use the time value of money concept. The formula for compound interest is:

$FV = PV (1 + r)^n$

where:

• $FV$ = future value
• $PV$ = present value
• $r$ = monthly interest rate
• $n$ = number of months

We will bring all payments to the reference point, which is 6 months from now.

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Step 1: Convert Given Interest Rate to Monthly Rate

The annual interest rate is 4.3% compounded monthly, so the monthly interest rate is:

$r = \frac{4.3\%}{12} = \frac{0.043}{12} = 0.00358333$

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Step 2: Convert Given Payments to the Reference Time (6 months from now)

Payment 1: $700 (due 4 months ago)

Since this payment was due 4 months ago, it is effectively 10 months behind the reference time (6 months from now). We compound it forward by 10 months:

$FV_1 = 700 (1.00358333)^{10}$

$FV_1 = 700 \times 1.036746$

$FV_1 \approx 725.72$

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Payment 2: $1000 (due in 12 months)

This payment is due 6 months after the reference time, so we discount it back by 6 months:

$FV_2 = 1000 (1.00358333)^{-6}$

$FV_2 = 1000 \times 0.978546$

$FV_2 \approx 978.55$

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Step 3: Compute the Equivalent Single Payment

The equivalent payment at the 6-month mark is:

$X = FV_1 + FV_2$

$X = 725.72 + 978.55$

$X = 1704.27$

Thus, the economically equivalent single payment is $1704.27.

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Final Answer:

$\boxed{1704.27}$

Would you like a breakdown of another method or more details?

Here are five related questions for further exploration:

1. What would be the equivalent payment if the interest was compounded quarterly instead of monthly?
2. How does changing the reference time affect the equivalent payment calculation?
3. What if one of the payments was missing? How would that affect the solution?
4. How would the calculation change if the interest rate was 6% instead of 4.3%?
5. Can we solve this problem using present value (PV) instead of future value (FV)?

Tip: Always make sure to adjust past and future payments to the same point in time when comparing their economic value.