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Linda O’Shay deposited $30,000 in a savings account as a perpetual trust. She believes the account will earn 7% annual interest during the first 10 years and 5% interest thereafter. The trust is to provide a uniform end-of-year scholarship at the university. What uniform amount could be used for the student scholarship each year, beginning at the end of the first year and continuing forever?

Respuesta :

Answer:

The uniform amount that can be used for scholaship, every year, first being at the end of the first year is $1,745.14

Explanation:

Hi, in order to find the amount that can be used to pay for school so the balance would last forever, given that $30,000 were left in the savings account, we need to solve for A the following equation.

[tex]PresentValue=\frac{A((1+r_{1} )^{n}-1) }{r_{1}(1+r_{1})^{n} } +\frac{A}{(r_{2})} \frac{1}{(1+r_{1})^n}[/tex]

Where;

r1 = 7%

r2 = 5%

n = 10

PresentValue = $30,000

Everything should look like this:

[tex]30,000=\frac{A((1+0.07)^{10}-1) }{0.07(1+0.07)^{10} } +\frac{A}{(0.05)} \frac{1}{(1+0.07)^10}[/tex]

[tex]30,000=A(7.023581541)+A(10.16698584)[/tex]

[tex]30,000=A(17.19056738)[/tex]

[tex]A=1,745.14[/tex]

So, uniform amount that could be used for the student scholarship each year, beginning at the end of the first year and continuing forever is $1,745.14

Best of luck.

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