Question

a firm purchases equipment issuing an interest-bearing note that calls for 12 annual payments of $35,917. the first payment is due immediately. the note bears interest at 6% apr. determine the original cost of the equipment. note:

Answer 1

The original cost of the equipment is calculated using the present value of an annuity due formula. An immediate first payment characteristic of the annuity due requires the formula to be adjusted, which after computation will give the correct original cost.

Step-by-step explanation:

The original cost of the equipment can be determined using the concept of the present value of an annuity since the payments are made at regular intervals. In this scenario, we have an immediate first payment, which is a characteristic of an annuity due. To calculate the present value of an annuity due, you need to adjust the present value formula for an ordinary annuity to account for the immediate first payment.

The formula for the present value of an annuity due is Present Value = Payment x [(1 - (1 + interest rate)^(-number of payments + 1)) / interest rate] x (1 + interest rate). We know that the annual payment is $35,917, the interest rate per period is 6%, and there are 12 payments. Plugging these values into the formula will give us the original cost of the equipment:

Present Value = $35,917 x [(1 - (1 + 0.06)^(-11)) / 0.06] x (1 + 0.06)

= $35,917 x [1 - (1 + 0.06)^(-11) / 0.06] x 1.06

Note that the payment is multiplied by 1.06 because the first payment is made immediately and thus does not need to be discounted.