Three years ago, you deposited some money in your bank account.

Question

Two years from today you will withdraw $3,000 from your bank account. You will withdraw a further $6,000 three years from today after which you will have nothing left over in your account. These are the only deposits and withdrawals that you make. The bank pays an interest of 9% compounded quarterly. a) How much did you deposit three years ago?

Answer 1

First, you need to compute your EAR. 9% interest compounded quarterly results in a 9.31% EAR. The formula for EAR is:

EAR = (1+r/n)^n-1

R is the stated rate (9%)

N is the number of compounding periods (4)

The PV of your deposit today has to equal the PV of your withdrawals. The PV of the $6,000 withdrawal in year 6 is 6000/((1+.0931)^6) = $3,517.48. The PV of the $3,000 withdrawal in year 5 is 3000/((1+.0931)^5) = $1,922.45. The sum of those two is $5,439.93, which is the amount you must initially deposit.