Question related to perpetual annuity.
As part of its CSR initiative, Jim Pizza decides to donate $10000 to the National Fast Food Institute every year till the company lasts starting from 2011. To do the same how much do they have to set aside from their profits in 2010 if we assume the rate of interest is 4%?
As the company has decided to pay $10000 every year till the company exists, we can consider the amount is given every year for perpetuity as any company is supposed to have a perpetual existence.
Now the rate of interest is given as 4%. This means that an amount X that we have today will be equal to X*(1 + 4%) ^n = X*(1.04) ^n after n years. Conversely an amount X after n years is presently equal to X/ (1.04) ^n. This is called the present value of the amount.
To determine how much the company has to set aside from its profits this year to be able to offer the annual donation, we have to determine the present value of all future donations and take their sum.
So the amount needed A = 10000/1.04 + 10000/ (1.04) ^2 +…
=> 10000[1.04^-1 + 1.04^-2 +…]
Now the sum 1.04^-1 + 1.04^-2 +… = 1/.04 = 100/4 = 25
=> A = 10000*25 = 250,000
Therefore the company needs to set aside just $250,000 for a perpetual annual donation of $10,000 every year.