What lump sum of money must be deposited into a bank account

What lump sum of money must be deposited into a bank account at the present time so that $600 per month can be withdrawn for six years, with the first withdrawal scheduled for seven years from today? The interest rate is 1/2% per month. (Hint: Monthly withdrawals begin at the end of the month 84.)

Solution

The total amount to be deposited should be $41,717.79 or in round figures $41,718.

As the question calls for a lump sum amount and the first withdrawal is after 7 years. We will take time for 7 years or 84 months. The amount can be calculated by multiplying $600 by 72. As the person wants to withdraw $600 for 6 years i.e. 72 months. that is a total of $43,200. The interest rate is given as 1/2 % or we can write it as 0.5%.

Putting the values in formula

P = A / (1 + r/100)^t

P = 43,200 / (1 + 0.5 ) ^ 7

On solving we get $41,717.79.