5.2 Withdrawing from a Savings Account
Learning Outcomes
Calculate the payment size and interest earned for regular withdrawals from a savings account.
It is also possible to make regular withdrawals from a savings account. When you make these regular withdrawals, you’re deducting from the money you’ve built up in the account. At the end of the annuity (when the account is closed), all remaining funds (FV) will need to be withdrawn. If nothing is specified for a remaining $ amount, assume it is zero.
| PV | Interest | PMT | FV |
|---|---|---|---|
| Initial Deposit | + % Gain | = Regular Withdrawals | + Final Withdrawal |
| + | + | − | 0 or − |
A common example where these type of regular withdrawals are made is a retirement fund where the retiree withdraws a certain amount of money every month to pay their bills or an education account where a student withdraws money twice a year to pay their tuition.
See the sections below for key formulas, tips and examples related to calculations when withdrawing from a savings account.
Calculating the Payment Size
Let us start by calculating the size of your regular withdrawals (PMT) from an education fund. It is possible that there is an ending balance (FV) or nothing leftover at the end (FV = 0). We will examine both scenarios — when you have no money leftover and when you have an ending balance.
EXAMPLE 5.2.1
Your have $20,000 in your savings account to pay for your post-secondary education. You plan on making semi-annual withdrawals from the account for three years while you attend BCIT. The first withdrawal will be in six months. The savings account will earn 4%, compounded monthly. What will be the size of your semi-annual withdrawals?
| B/E | P/Y | C/Y | N | I/Y | PV | PMT | FV |
|---|---|---|---|---|---|---|---|
| END | 2 | 12 | 3×2=6 | 4 | +20,000 | CPT −3,572.53 | 0 |
Why is B/E set to END? This is because the first withdrawal is being made in six months, at the end of the first payment interval. Semi-annual payments are payments that occur twice per year or once every six months. Again, we do not need to anything in the calculator (it is set to END by default).
Why does P/Y equal 2? The payments are semi-annual, or twice per year.
Why does C/Y equal 12? The account earns 4% compounded monthly (12 times per year).
Note that P/Y and C/Y are not equal in this example. When P/Y ≠ C/Y, we call this a general annuity.
Why does N equal 6? N equals six because you will make semi-annual withdrawals for 3 years. This will give you a total of 3×2 withdrawals. Remember that N = number of years × P/Y = total number of withdrawals.
Why does PV equal +20,000? The initial balance (or deposit) will be equal to PV and in this example, that initial balance equals $20,000. In this text, we will treat that initial balance (or deposit) as positive.
Finally, why does FV equal 0? Since all of the money will be withdrawn, FV = 0.
Now we can calculate the size of your withdrawals (PMT). Notice that the BAII Plus will give us a negative value for the payments. This minus sign (negative sign) indicates that the payments (PMT) are reducing the balance in the account until it eventually gets to zero (FV = 0). We will drop this minus sign (negative sign) for our final answer.
Conclusion: You will be able to withdraw $3,572.53 from your savings account every six months.
Check Your Knowledge 5.2.1
What if you wanted to have $3,000 remaining at the end of three years to travel after you graduate? Redo the above example but instead, have an ending balance of $3,000 remaining in the account. What will be the size of your regular withdrawals? Drag in the values that you would enter in your calculator.
Conclusion: You will be able to withdraw $3,097.16 from your savings account every six months. Note that PMT and FV have the same sign (both negative). You can consider them both as withdrawals. We are withdrawing $3,097.16 every six months and withdrawing $3,000 from the account at the end of three years.
Calculating the Interest Earned
For all investments, again, interest is the difference between money in and money out.
[latex]\begin{align*} \textrm{Interest} &= \textrm{Money Out} - \textrm{Money In} = \textrm{\$ OUT} - \textrm{\$ IN} \end{align*}[/latex]
In the case of annuities with regular withdrawals, we consider the initial deposit, PV, to be money in ($ IN) because this money is being deposited into the account. We consider the regular withdrawals, PMT, to be money out ($ OUT) because they are being withdrawn from the account. Finally, we consider FV (if there is any balance remaining at the end) to be money out ($ OUT) because we assume that the final amount (if it’s not 0) will be withdrawn from the account when the account is closed.
| PV | Interest | PMT | FV |
|---|---|---|---|
| Initial Deposit | + % Gain | = Regular Withdrawals | + Final Withdrawal |
| $ IN | $ IN | $ OUT | $ OUT |
This gives us the following equation for the interest earned:
[latex]\begin{align*} \textrm{Interest Earned} &= \textrm{\$ OUT} - \textrm{\$ IN}\\ &=(\textrm{Regular Withdrawals}+\textrm{Final Withdrawal}) - \textrm{Initial Deposit}\\ &= ( \textrm{PMT}\times\textrm{N}+\textrm{FV})-\textrm{PV} \end{align*}[/latex]
Check Your Knowledge 5.2.2
Key Takeaways
Key Takeaways: Regular Withdrawals from Saving Accounts
Your Own Notes
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Payments that occur twice per year or once every six months.
An Annuity where P/Y ≠ C/Y
