Bryan had to pay his friend $710.00 that was due 4 months ago and $470.00 in 2 months. If his friend was charging him an interest rate of 1.00% p.m., what single payment now would settle both payments? Choose 'today' as the focal date.

To find the single payment Bryan needs to make today to settle both debts, we will use the concept of present value, given the monthly interest rate of 1.00% (or 0.01 as a decimal). The payments must be discounted to the focal date, which is today. The formula for present value is:

\[
PV = \frac{F}{(1 + i)^n}
\]

Where:
- $ PV $ = Present Value (amount today)
- $ F $ = Future payment
- $ i $ = Interest rate per period (monthly in this case)
- $ n $ = Number of periods (months)

### 1. The first debt ($710.00) was due 4 months ago:
This debt should be compounded forward by 4 months to today:
\[
PV_1 = 710 \times (1 + 0.01)^4 = 710 \times 1.04060401
\]
\[
PV_1 = 738.83
\]

### 2. The second debt ($470.00) is due in 2 months:
This debt should be discounted back by 2 months to today:
\[
PV_2 = \frac{470}{(1 + 0.01)^2} = \frac{470}{1.0201}
\]
\[
PV_2 = 460.70
\]

### 3. The total present value:
The total payment Bryan should make today is the sum of the present values:
\[
PV_{\text{total}} = 738.83 + 460.70 = 1,199.53
\]

### Answer:
Bryan should make a single payment of **$1,199.53** today to settle both debts.

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Would you like further details or have any questions about this solution?

Here are some additional questions you could explore:
1. What would the total payment be if the interest rate was 2.00% p.m.?
2. How does changing the number of months affect the present value calculation?
3. What happens if Bryan pays the first debt 6 months late instead of 4 months?
4. How is the formula for present value different for annual interest rates?
5. What if Bryan’s friend was charging simple interest instead of compound interest?

**Tip:** Always remember to convert percentages into decimals when using formulas!

Discover how to calculate the single payment Bryan should make today to settle his two debts, using a 1.00% monthly interest rate. This problem involves the use of present value and compound interest formulas. Ideal for students in Grades 10-12.

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