Miller and Associates will need to pay $8,426.52 into the sinking fund each period to pay back the loan at the end of 10 years, assuming a rate of 10% compounded semiannually.
The Breakdown
To calculate the amount that needs to be paid into the sinking fund each period, we can use the sinking fund formula:
P = (A × ((1 + r/n)^(n×t) - 1)) / (r/n)
Where:
P = periodic payment
A = loan amount
r = annual interest rate (as a decimal)
n = number of compounding periods per year
t = number of years
In this case, A = $160,000, r = 0.10, n = 2 (since interest is compounded semiannually), and t = 10.
Plugging in the values, we get:
P = ($160,000 × ((1 + 0.10/2)(²×¹⁰) - 1)) / (0.10/2)
P = ($160,000 × (1.05²⁰ - 1)) / 0.05
P = ($160,000 × 2.6533) / 0.05
P = $8,426.52
Therefore, Miller and Associates will need to pay $8,426.52 into the sinking fund each period to pay back the loan at the end of 10 years, assuming a rate of 10% compounded semiannually.