Question

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?

Answer 1

To find the uniform amount for the student scholarship, we can calculate the present value of the perpetual stream of payments using the formula for the present value of a perpetuity. The uniform amount is $1,500.

Step-by-step explanation:

To find the uniform amount that could be used for the student scholarship each year, we can calculate the present value of the perpetual stream of payments. For the first 10 years, the account earns 7% interest.

After that, it earns 5% interest. We can use the formula for the present value of a perpetuity:

PV = C / r

where PV is the present value, C is the annual payment, and r is the interest rate. Substituting the values, we get:

PV = C / 0.07

For the perpetuity to be equal to $30,000, we solve for C:

C / 0.05 = $30,000

C = $30,000 * 0.05 = $1,500

Therefore, the uniform amount that could be used for the student scholarship each year is $1,500.

Answer 2

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

Step-by-step 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.

`PresentValue=(A((1+r_(1) )^(n)-1) )/(r_(1)(1+r_(1))^(n) ) +(A)/((r_(2))) (1)/((1+r_(1))^n)`

Where;

r1 = 7%

r2 = 5%

n = 10

PresentValue = $30,000

Everything should look like this:

`30,000=(A((1+0.07)^(10)-1) )/(0.07(1+0.07)^(10) ) +(A)/((0.05)) (1)/((1+0.07)^10)`

`30,000=A(7.023581541)+A(10.16698584)`

`30,000=A(17.19056738)`

`A=1,745.14`

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.