Question

A perpetuity is similar to a decreasing annuity, except that the payments continue forever. A grateful alumnus decides to donate a permanent scholarship of $1440 per year. How much money should be deposited in the bank at 8% interest compounded annually in order to be able to supply the money for the scholarship at the end of each year?

Answer 1

Since it is compounded each year, and 1440 is then taken out, only 1440 needs to be the interest. We are assuming the minumum, so $1440 tops. This means that the relationship is: \[8/100 = 1440/x\] so \[x=1440/(8/100) = 1440(100)/8 = 144000/8 = 18000\] thus he needs to deposit 18000.