Question

Suppose $1,000,000 fund is established for a scholarship program in a school. Assume that the amount is deposited in a long-term saving bank account that pays 6.75% yearly continuous interest rate with agreement that $15,000 will be withdrawn at the end of each year. Write a model whose solution predicts total balance in the bank after t years. Obtain the solution. Is this scholarship program sustainable?

Answer 1

deposited $10,000,00 with an interest of 6.75 % ,with an yearly withdrawal of $ 15000

calculation ;-

first year (+) interest @ 6.75 % (-) withdrawal	$ 10,000,00 (+ )$ 67500 = 10,67500 (-)$ 15000 = 10,52500
second year b/d (+) interest @ 6.75 % (-) withdrawal	$ 10,52500 (+) $ 71043.7 = 11,23543.7 (-) $ 15000 = 11,08543.7
third year b/d (+) interest @ 6.75 % (-) withdrawal	$ 11,8543.7 (+) $ 74,826   = 11,83,370.3 (-) $ 15000 = 11,68370.3
fourth year b/d (+) interest @ 6.75 % (-) withdrawal	$ 11,68370.3 (+) $ 78,280.8 = 12,46,651.1 (-) $ 15000 = 12,31,651.1
fifth year b/d	$ 12,31,651

the bank balance computation will gon on as shown in the above table. from the above calculation we can conclude that , the scholarship programe is sustainable.Because the interest will increase as per the balance increases so the amount will go up.