Question

ou have an account that pays 3% annual interest compounded monthly. You make an initial deposit, and then withdraw $170 at the end of each month for 6 years. At that time you make a second deposit of $9000, and then withdraw $250 at the end of each month for the following 8 years, ending with a zero balance. What is your initial deposit?

Answer 1

First, we calculate the amount in account at the end of 6 years (after depositing $9,000).  

Amount in account at the end of 6 years (after depositing $9,000) is calculated using PV function in Excel :

rate = 3%/12 (converting annual rate into monthly rate)

nper = 8*12 (8 years of withdrawals with 12 withdrawals each year)

pmt = -250 (monthly withdrawal. This is entered with a negative sign because it is a cash outflow)

PV is calculated to be $21,313.65

Amount in account before depositing $9,000 =  $21,313.65 - $9,000 = $12,313.65

Initial deposit is calculated using PV function in Excel :

rate = 3%/12 (converting annual rate into monthly rate)

nper = 6*12 (6 years of withdrawals with 12 withdrawals each year)

pmt = -170 (monthly withdrawal)

fv = -12313.65 (amount remaining in account at end of 6 years)

type = 0 (each withdrawal is at the end of the month)

PV is calculated to be $21,476.40

Initial deposit is $21,476.40