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?

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.