Question

Aloma, a university graduate who started a successful business, wants to start an endowment in her name that will provide scholarships to IE students. She wants the scholarship to provide $10,000 per year and expects the first one to be awarded on the day she fulfills the endowment obligation. If Aloma plans to donate $100,000, what rate of return must the university realize in order to award the $10,000 per year scholarship forever

Answer 1

Rate of return is the rate of interest paid on unpaid balance of money which is borrowed or the interest rate earned on the unrecoverable balance of the money lent or investment.

Annual Payment
`A = F[(i)/((1+i)^(2) -1)]` where F is accumulated sum of amount, n is number of years and i is annual rate of interest. The standard notation equation is A = F(A/ F, i, n)

Annual Payment
`A = P[(i(1+i)^(2) )/((1+i)^(2) -1)]` where P is present value, n is number of years and i is annual rate of interest. The standard notation equation is A = P(A/P,i.n)

IRR (first_celtlast_cell) represent the internal rate of return for series of cash flow.

The scholarship starts as soon as endowment obligation are fulfilled so here P is 100000 - 10000 = 90000, A is 10000, n is infinite. So, the equation is

0 = -90000 + 10000 /
`i^(*)`

`i^(*)` = 0.1111

OR

`i^(*)` = 11.11%