Question

Oriole Inc. has completed the purchase of new Dell computers. The fair value of the equipment is $890,082. The purchase agreement specifies an immediate down payment of $216,000 and semiannual payments of $83,108 beginning at the end of 6 months for 5 years. What is the interest rate, to the nearest percent, used in discounting this purchase transaction

Answer 1

• Annual rate = 8%
• Semiannual rate = 4%

Step-by-step explanation:

The present value of the amount that is to be paid periodically:

= Fair value - Down payment

= 890,082 - 216,000

= $674,082

This is a semi annual payment so the variables need to be converted as such:

Period = 5 years * 2 = 10 semi annual periods

This payment is constant so it is an annuity.

Present value of annuity = Annuity * Present value interest factor, 10 periods, x percent

674,082 = 83,108 * Present value interest factor, 10 periods, x percent

Present value interest factor, 10 periods, x percent = 674,082 / 83,108

= 8.1109

If checked in the PVIFA Table, 8.1109 at 10 periods corresponds with 4%.

The annual interest rate is therefore:

= 4% * 2

= 8%