Grouper Inc. has completed the purchase of new Dell computers. The fair value of the equipment is $675,803. The purchase agreement specifies an immediate down payment of $164,000 and semiannual payments of $63,101 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?

The interest rate, to the nearest percent, used in discounting this purchase transaction 8%.

Explanation:

The interest rate can be calculated using the following RATE function in Excel:

Interest rate = RATE(nper,pmt,-pv,fv,type)*n (1)

Where;

nper = number of periods = number of years to maturity * number of semiannual in a year = 5 * 2 = 10

pmt =  semiannual payments = $63,101 = 63101

pv = present value = fair value balance = fair value - immediate down payment = $675,803 - $164,000 = $511,803 = 511803

fv = future value = desired cash balance after last payment = 0

type = when payments are due (0 = end of period. 1 = beginning of period) = 0

n = number of compounding period per year = number of semiannual in a year = 2

Substituting the values into equation (1), we have:

Interest rate = RATE(10,63101,-511803,0,0)*2 (2)

Inputting =RATE(10,63101,-511803,0,0)*2 into an excel sheet (Note: as done in the attached excel file), the Interest rate is obtained as 8.00%.

Therefore, the interest rate, to the nearest percent, used in discounting this purchase transaction 8%.

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