As a budding songwriter, which you do in addition to studying engineering, you’ve written the hit new Christmas pop song. You’ve started to receive annual royalty payments, paid at the end of each year, for your work. However, you realize that success in the music business can be short-lived and want to invest your royalties while the song is popular (and therefore you are receiving the largest royalty payments). After talking with your network of Christmas songwriters, a small but wealthy group, you estimate that you’ll continue to receive royalty checks for the next 12 years, after which everyone will have tired of the song and the royalty checks will end. You anticipate receiving royalties in the amount of $150,000 at the end of the first year, after which the amount will decrease by $10,000 each year. Further, you have decided to invest all of your royalties in an account that earns 8% interest compounded annually.

(a) What is the future value of this royalty payments?

(b) Instead of the normal payment plan, with declining payments over 12 years, the record company has offered to pay you in equal amounts each year. Based upon the provided information, how much would you receive each year (i.e. each payment) under this revised payment plan?