Final answer:
The compound discount on $8800 due in 7.5 years at a 9.6% interest rate compounded monthly is approximately $9,077.50, calculated using the future value formula for compound interest and subtracting the present value from the future value obtained.
Step-by-step explanation:
To determine the compound discount on $8800 due in 7.5 years with an interest rate of 9.6% compounded monthly, we first need to calculate the future value of the amount using the formula for compound interest: FV = P(1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
Substitute the given values into the formula to get:
FV = 8800(1 + 0.096/12)^(12 * 7.5)
Next, calculate the future value:
FV = 8800(1 + 0.008)^(90) = 8800 * (1.008)^90 ≈ $17,877.50
Now, to find the compound discount, subtract the present value (the amount due today, which is $8800) from the future value we just calculated.
Compound Discount = Future Value - Present Value
Compound Discount = $17,877.50 - $8800 ≈ $9,077.50
The compound discount on $8800 due in 7.5 years at a 9.6% interest rate compounded monthly is approximately $9,077.50.