Question

An author just signed a lucrative contract with a publisher that offers to pay her the amount of $500 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 7%.

Answer 1

Answer:

Ans. The annuity that will be equivalent to the publisher´s advance would be $26.40 per year, for 9 years at 7% interest rate.

Explanation:

Hi, first, let´s bring that $500 to be paid in 9 years to present value, we need to use the following formula.

$PresentValue=\frac{FutureValue}{(1+r)^{n} }$

Where: r is our discount rate (7%) and n the periods from now when she will receive that $500 amount. This should look like this.

$PresentValue=\frac{500}{(1+0.07)^{9} } =271.97$

Ok, so the equivalent amount of money today of those $500 in nine years is $271.97, but the author wants $100 today so the remaining amount has to be used to find the equal annual payments to be made in order to be equivalent to re remaining balance ($171.97). We now need to use the following equation.

$Present Value=\frac{A((1+r)^{n}-1 )}{r(1+r)^{n} }$

And we solve for "A" like this

$171.97=\frac{A((1+0.07)^{9}-1 )}{0.07(1+0.07)^{9} }$

$171.97=\frac{A(0.838459212 )}{0.128692145}$

$171.97=A(6.515232249)$

$A=\frac{171.97}{6.515232249} = 26.40$

Therefore, the equivalent amount of money of $500 in 9 years is $100 today and $26.40 every year, at the end of the year, for nine years.

Best of luck.