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?

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 Since all of the money will be withdrawn, FV = 0.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.

For all investments, again, interest is the difference between money in and money out.

$\begin{align*} \textrm{Interest} &= \textrm{Money Out} - \textrm{Money In} = \textrm{\$ OUT} - \textrm{\$ IN} \end{align*}$

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.

This gives us the following equation for the interest earned:

$\begin{align*} \textrm{Interest Earned} &= \textrm{\$ OUT} - \textrm{\$ IN}\\ &=(\textrm{Regular Withdrawals}+\textrm{Final Withdrawal}) - \textrm{Initial Deposit}\\ &= ( \textrm{PMT}\times\textrm{N}+\textrm{FV})-\textrm{PV} \end{align*}$

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