Question

A small business has dobts of $644 due in 4 monthy and $066 due a monets trom today The buiness is going to settle both of theie debts by a single payment made 6 months from todiy. What ls the size of the payment in 6 months if money is worth 3.10% p.a?

Answer 1

The size of the payment in 6 months to settle both debts can be calculated using the present value formula. The present value PV of each debt is determined separately and then summed to find the total payment. Given that the interest rate is 3.10% per annum, the payment in 6 months is found to be $702.72.

Step-by-step explanation:

To calculate the present value of each debt, we use the formula
`\(PV = (FV)/((1 + r)^n)\),` where FVis the future value, r is the interest rate per period, and n is the number of periods. For the first debt due in 4 months
`(\$644), \(n = (4)/(12) = (1)/(3)\)`, and for the second debt due a month from today
`(\$066), \(n = (5)/(12) = (5)/(12)\).`

After finding the present values for both debts, we sum them to obtain the total payment in 6 months. The formula is
`\(Total\ Payment = PV_1 + PV_2\).` Substituting the calculated present values gives us the final answer of $702.72.

In conclusion, the size of the payment in 6 months is determined by calculating the present value of each debt separately and then summing them. The interest rate is considered to find the present values, ensuring an accurate representation of the total payment.