An author just signed a lucrative contract with a publisher that offers to pay her the amount of $600 at the end of year 9 when the book is scheduled to be released. The author, being profligate, desires to receive a different package: an immediate payment of $100 that is followed by an annuity (an equal amount) to be paid at the end of each year for 9 consecutive years. What annuity will make his package equivalent to the publisher's advance. Use an interest rate is 6%.

Question

Essence Fritz

Business

16 November, 14:19

An author just signed a lucrative contract with a publisher that offers to pay her the amount of $600 at the end of year 9 when the book is scheduled to be released. The author, being profligate, desires to receive a different package: an immediate payment of $100 that is followed by an annuity (an equal amount) to be paid at the end of each year for 9 consecutive years. What annuity will make his package equivalent to the publisher's advance. Use an interest rate is 6%.

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Teagan Sexton · Answer 1

annuity = $37.51

Explanation:

future value of the annuity = $600 - future value of the initial $100 paid

$100 x 1.06⁹ = $168.95

future value of the annuity = $600 - $168.95 = $431.05

FV of an annuity = payment x {[ (1 + r) ⁿ - 1] / r}

payment = FV / {[ (1 + r) ⁿ - 1] / r}

FV = $431.05 r = 6% n = 9

payment = $431.05 / {[1.06⁹ - 1] / 0.06} = $431.05 / {0.68948 / 0.06} = $431.05 / 11.4913 = $37.51