Final answer:
To settle a future debt of $3000 with an annual interest rate of 10.5% compounded semi-annually, Tim would need to pay approximately $2456.37 today.
Step-by-step explanation:
To settle a debt of $3000 that is due two years from now with an interest rate of 10.5% per annum compounded semi-annually, we need to calculate the present value of that future sum. To do this, we use the formula for the present value of future money:
PV = FV / (1 + r/n)nt
Where:
PV = Present Value
FV = Future Value ($3000)
r = Annual interest rate (10.5%, or 0.105)
n = Number of times interest is compounded per year (2 for semi-annually)
t = Time in years (2 years)
The calculation will be as follows:
PV = 3000 / (1 + 0.105/2)2*2
PV = 3000 / (1.0525)4
PV = 3000 / 1.2211
PV ≈ $2456.37
Therefore, Tim would need to pay approximately $2456.37 today to settle his entire debt of $3000 due two years from now at the given compound interest rate.