You are planning to make 18 monthly withdrawals beginning at the end of the sixth month. You plan to withdraw $119 in the sixth month and increase your withdrawals by $19 over the previous month’s withdrawal. How much should you deposit now in a bank account that pays 12% per year compounded monthly?

We need to deposit $2,163.45 now.

Explanation:

Withdrawal 1st to 6th : $119 per

Withdrawal 7th to 18th: $138 per (= 119 + 19)

Rate: 1% per month (= 12% per year/ 12 month)

We use the formula PV in excel to calculate the deposit required now = PV(rate, number of withdrawal, withdrawal amount per)

Because the amount in all withdrawal are not same, then we need to do 4 steps:

Firstly, we need to calculate PV of 6 withdrawal of $119 per = PV(1%,6,119) = $689.66

Secondly, we need to calculate PV (at the 7th month) of 12 withdrawal of $139 per = PV(1%,12,139) = $1,564.46

Then we need to calculate PV (at 1st month) of $1,564.46 = $1,564.46/(1+1%)^6 = $1,473.79

Final, Total deposit = $689.66 +$1,473.79 = $2,163.45

Please see excel for more details & testing for the withdrawals in 18 months