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

Quizplus · Accepted Answer

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 0.9756

So, for each semiannual payment of $4,000, the present value is:

PV = $4,000 x 0.9756 x 0.8638 = $3,275.48

To 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 24.7835

So, the total present value of all payments is:

PV = $4,000 x 24.7835 = $99,134

However, 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 1.3450

So, the interest on each semiannual payment is:

Interest = $4,000 x 1.3450 - $4,000 = $540

And the total interest over the life of the note is:

Interest = $540 x 24 = $12,960

Therefore, the cost of the machine is:

Cost = PV - Interest = $99,134 - $12,960 = $86,174

Rounding to the nearest cent, the answer is B) $20,302.80

Pelcher Company Acquires a Machine by Issuing a Note That (Use appropriate factor(s)from the tables provided.)\bold{\text{(Use appropriate factor(s)from the tables provided.)}}(Use appropriate factor(s)from the tables provided.)

Pelcher Company Acquires a Machine by Issuing a Note That $\bold{\text{(Use appropriate factor(s)from the tables provided.)}}$