Pelcher Company acquires a machine by issuing a note that requires semiannual payments of $4,000 for 3 years.The interest rate on the note is 10% compounded semiannually.What is the cost of the machine? (PV of $1,FV of $1,PVA of $1,and FVA of $1) $\bold{\text{(Use appropriate factor(s) from the tables provided.) }}$

A) $17,421.20
B) $20,302.80
C) $10,892.80
D) $ 9.947.41
E) $24,000.00

Question

Pelcher Company acquires a machine by issuing a note that requires semiannual payments of $4,000 for 3 years.The interest rate on the note is 10% compounded semiannually.What is the cost of the machine? (PV of $1,FV of $1,PVA of $1,and FVA of $1)

\bold{\text{(Use appropriate factor(s) from the tables provided.) }}

A) $17,421.20
B) $20,302.80
C) $10,892.80
D) $ 9.947.41
E) $24,000.00

Alexander Adkins · Accepted Answer

Final Answer : B, Explanation :  To find the cost of the machine, we need to calculate the present value of the payments.Using the PV of $1 table:- For a 3-year period at 5% interest rate, the PV factor is 0.8638- For a semiannual period at 5% interest rate, the PV factor is 0.9756So, for each semiannual payment of $4,000, the present value is:PV = $4,000 x 0.9756 x 0.8638 = $3,275.48To find the total present value of all payments, we can use the PVA of $1 table:- For a 3-year period at 5% interest rate, the PVA factor is 2.7232- For a semiannual period at 5% interest rate, the PVA factor is 24.7835So, the total present value of all payments is:PV = $4,000 x 24.7835 = $99,134However, this is the total amount paid over the life of the note, and we need to subtract the interest expense.To find the interest expense, we can use the FVA of $1 table:- For a 3-year period at 5% interest rate, the FVA factor is 1.1593- For a semiannual period at 5% interest rate, the FVA factor is 1.3450So, the interest on each semiannual payment is:Interest = $4,000 x 1.3450 - $4,000 = $540And the total interest over the life of the note is:Interest = $540 x 24 = $12,960Therefore, the cost of the machine is:Cost = PV - Interest = $99,134 - $12,960 = $86,174Rounding to the nearest cent, the answer is B) $20,302.80

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