Question

An amount of P 250,000 is now deposited into a savings account that earns 12% compounded continuously for the school requirements of a civil engineering student on the succeeding 5 years from now. If the every year the student will withdraw P 51,651 from this account, how many years would the deposit lasts?

Answer 1

The Initial amount P = 250000

The compound interest rate (r) is 12 % and for succeeding 5 years.

The amount that the student withdraw every year P = 51651

Compounded annually P = Pintial (1+r) n

So for the first year the amount increment is 250000(1+0.12) = 280000

After withdrawal amount remain in the account is 280000-51651 = 228349

After second year the amount increment is 228349(1+0.12) = 255750.88

After withdrawal 255750.88 – 51651 = 204099.88

After third year = 204099.88(1+0.12) = 228591.8656

After withdrawal 228591.8656 – 51651 = 176940.8656

After fourth year = 176940.8656 (1+0.12) = 198173.7695

After withdrawal fourth time = 198173.7695 – 51651 = 146522.77

After fifth year increment = 146522.7695(1+0.12) = 164105.51

After withdrawal Fifth year = 164105.5018 – 51651 = 112454.51

5 years after no compound increment of money from the bank but student continue his withdrawal amount every year

After 6th year the amount held in account = 112454.51– 51651 = 60803.51

Next year after withdrawal = 60803.51 – 51651 = 9152.51

After 7 years the amount remaining in the student account is 9152.51. So the account lasts for 7 years with the final balance of the above amount.