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Miller and Associates borrowed $160,000. The company plans to set up a sinking fund that will pay back the loan at the end of 10 years. Assuming a rate of 10% compounded semiannually, what amount is to be paid into the fund each period?

User Ywenbo
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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.

User KostasC
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