Question

Question 4 20 pts If you deposit $1,000 in periods 9, 10 and 11 how much will you be able to withdraw (the same amount in each period) in periods 11 and 12 to just empty your bank account, if your account earns 2% compound annually? (Hint: Bring all the cash-flows to today and then solve from there) 0 $1,040 O $1,485 O $1,560 0 $1,623 0 $1,545

Answer 1

Answer is $1,545

Deposit in year 9 = $1,000
Deposit in year 10 = $1,000
Deposit in year 11 = $1,000

Interest rate = 2%

Let withdrawal in year 11 and year 12 be $x

Accumulated value at end of year 11 = $1,000*1.02^2 + $1,000*1.02 + $1,000
Accumulated value at end of year 11 = $1,000 * 1.0404 + $1,000 * 1.02 + $1,000
Accumulated value at end of year 11 = $3,060.40

Accumulated value at end of year 11 = Value of withdrawals at end of year 11
$3,060.40 = $x + $x/1.02
$3,060.40 = $x * 1.980392
$x = $1,545

So, withdrawals in periods 11 and 12 is $1,545