The Stack has just written and recorded the single greatest rock song ever made.

Question

The Stack has just written and recorded the single greatest rock song ever made. The boys in the band believe that the royalties from this song will pay the band a handsome $200,000 every year forever. The record studio is also convinced that the song will be a smash hit and the royalty estimate is accurate. The record studio wants to pay the band up front and not make any more payments for the song. What should the record studio offer the band if it uses a 5% discount rate, a 7.5% discount rate, or a 10% discount rate?

The band from the previous problem agrees to the one-time payment at a 5% discount rate, but it wants to figure the royalty payments from the beginning of the year, not the end of the year. How much more will the band receive??

Explanation / Answer

Amount of royalty forver = 200,000
Rate = 5%
Up front payment = 200,000/5% = 4,000,000

Rate = 7.5%%
Up front payment = 200,000/7.5% = 2,666,666.67

Rate = 10%
Up front payment = 200,000/10% = 2,000,000

One time Payment for annuity due = 200,000(1+5%) /5% = 4,000,000*(1.05) = 4,200,000

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