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!