Account is 200000 interest is 04 per month Monthly withdraw

Account is $200000, interest is 0.4% per month. Monthly withdraw is $1000. Find the num-

ber of months to deplete the account.

Solution

Starting amount = $200000

The interest will get deducted and then the amount will be withdrawn.

The last interest deducted will leave 1000 in the bank account to be withdrawn.

Value of last interest will be = 0.004*x

Such that, x - 0.004x = 1000

So x = 1004.016

Monthly interest deducted = 0.004(200000) + 0.004(200000 - 1000) + ......

Monthly interest deducted follows an arithmetic progression with difference = - 0.004*1000 = 4 and

start term = 0.004* 200000 = 800

So when the interest payment is < 4.016 for the first time, amount to be withdrawn will be less than or equal to 1000, and hence will be the last withdrawal.

So 800 + (n-1) * (-4) <4.016

n> 199.996

So n= 200