Twenty years ago, a generous alumnus donated $30,000 to Sudsville State College

Question

Twenty years ago, a generous alumnus donated $30,000 to Sudsville State College with the stipulation that the money be used to fund scholarships for a period of 15 years. The money has been sitting in an account earning an annual interest rate 3.8% compounded semiannualy for that entire 20 years, and now the institution is going to start making equal semiannual withdrawals from the account to distribute among various scholarhsips.

A.) How much can be withdrawn semiannualy so that after 15 years all of the money in the account is used up?

B.) Over the entire 35 year period, how much interest is earned by the money in the account?

Explanation / Answer

A.) How much can be withdrawn semiannualy so that after 15 years all of the money in the account is used up?

Present Value of $ 30000 = 30000*(1+3.8%/2)^(2*20)

Present Value of $ 30000 = $ 63,692.55

Amount to be withdrawn semiannualy = pmt(rate,nper,pv,fv)

Amount to be withdrawn semiannualy = pmt(3.8%/2,30,-63692.55,0)

Amount to be withdrawn semiannualy = $ 2804,91

B.) Over the entire 35 year period, how much interest is earned by the money in the account?

Interest is earned by the money in the account Over the entire 35 year period = (2804.91*30 ) - 30000

Interest is earned by the money in the account Over the entire 35 year period = $ 54,147.30

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