Respuesta :
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.
[tex]PresentValue=\frac{FutureValue}{(1+r)^{n} }[/tex]
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.
[tex]PresentValue=\frac{500}{(1+0.07)^{9} } =271.97[/tex]
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.
[tex]Present Value=\frac{A((1+r)^{n}-1 )}{r(1+r)^{n} }[/tex]
And we solve for "A" like this
[tex]171.97=\frac{A((1+0.07)^{9}-1 )}{0.07(1+0.07)^{9} }[/tex]
[tex]171.97=\frac{A(0.838459212 )}{0.128692145}[/tex]
[tex]171.97=A(6.515232249)[/tex]
[tex]A=\frac{171.97}{6.515232249} = 26.40[/tex]
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.
The amount of annuity that will make the package equivalent to publisher's advance would be $26.40, for 9 years at the rate of 7%.
What is a annuity?
Annuity is the series of payments made in equal installments. The annuity has a specific time and rate of interest.
To calculate the value of annuity, we first need to calculate the present value of $500 received after 9 years.
The present value can be calculated as follows:
[tex]\rm PV = FV\dfrac{1}{(1+r)^n}[/tex], where PV is the present value, FV is the future value, r is the rate of interest, and n is the number of years.
In the given question, FV is $500, r is 7%, and n is 9 years.
Therefore the PV of $500 received after 9 years at the interest rate 7% is:
[tex]\rm PV = \$500\dfrac{1}{(1+0.07)^9}\\\\\rm PV = \$500\dfrac{1}{(1.07)^9}\\\\\rm PV = \$500\dfrac{1}{1.838}\\\\\rm PV = \$271.97[/tex]
Therefore, the present value of $500 to be received after 9 years is $271.97. But the author desires to receive $100 immediately. Therefore, the annuity must cover the amount of $171.97.
The amount of $171.97 is the future value of the annuity after 9 years. To calculate the amount of annuity we need to calculate the amount of annuity, following formula will be used:
[tex]\rm PV =\dfrac{ A((1+r)^n-1)}{r(r+1)^n}[/tex], where A is the amount contributed per year, r is the rate of interest, and n is the number of years.
The above formula will be used to calculate the value A with PV of $171.97, rate 7% for 9 years.
The value of A will be:
[tex]\begin{aligned}\rm \$171.97 &=\dfrac{ A((1+0.07)^9-1)}{0.07(0.07+1)^9}\\\\\rm \$171.97 &=\dfrac{ A(0.83846)}{0.1287}\\\\\rm A &=\dfrac{(0.1287)(171.97)}{0.83846}\\\\\rm A &=\$26.40\end[/tex]
Therefore the annuity that will make the package equivalent is $26.40.
Learn more about annuity here:
https://brainly.com/question/1870035
