Question

Bonita Corporation bought a new machine and agreed to pay for it in equal annual installments of $5,410 at the end of each of the next 10 years. Assuming that a prevailing interest rate of 6% applies to this contract, how much should Bonita record as the cost of the machine?

Answer 1

To calculate the machine's cost, the present value of the equal annual installments at a 6% interest rate was found using the present value of an annuity formula. After calculations, Bonita Corporation should record approximately $39,836.09 as the cost of the machine.

Step-by-step explanation:

The student is asking how much Bonita Corporation should record as the cost of a machine when they agree to pay for it in equal annual installments over 10 years at a 6% interest rate. To find the present value of these installments, we use the formula for the present value of an annuity, as the payments are equal and occur at regular intervals.

The formula is:

`PV = Pmt x [(1 - (1 + r)^-n) / r]`

Where:

• Pmt is the annual payment ($5,410)
• r is the interest rate per period (6% or 0.06)
• n is the total number of periods (10 years)

Substituting the given values, we get:

`PV = $5,410 x [(1 - (1 + 0.06)^-10) / 0.06]`

After calculating, we get:

`PV = $5,410 x [(1 - (1 + 0.06)^-10) / 0.06] = $5,410 x 7.36009 ≈ $39,836.09`

Thus, Bonita Corporation should record approximately $39,836.09 as the cost of the machine.