4.7 Compound Interest with the BAII Plus

Using Financial Calculator Functions

The financial calculator recommended for this course is the BAII Plus.  Both this and other financial calculators have built-in compound-interest functions. It is possible to do almost all of the course calculations to the same accuracy without these functions, but the process is much faster if they are available.

The functions you will use in this chapter are controlled by the following keys:

In the same row is the PMT key which you will use in the next chapter. For this chapter, the PMT value should be set at 0.  It’s always best practice to set it to 0 each and every time!

Example 4.7.1

Invest $100 at j₂ =6%  for 4 years. N = 2× 4 = 8 periods.

We write this as:

Leaving some spaces for Annuities, in Chapter 5.

Example 4.7.2

To illustrate the use of the financial calculator, suppose you want to obtain the future value of a $5,000 loan at 8% compounded semi-annually for two years.

You will see the answer, $5,849.29, which was obtained earlier in the chapter by an account and by the formula. Note that the answer appears as a negative value on the calculator. This is because the calculator performs an equation of value in the form of:

[latex]\text{Value of Inflows}+\text{Value of Outflows}=0[/latex]

Hence it must make either inflows or outflows negative. (Since PV was made positive, it must make FV negative.)

From now on, you will normally indicate the procedure for solving problems – especially if they are likely to be done with computer functions – by listing the available values of the variables and what is required.

The answer would be negative on the calculator, but this will be mentioned only if confusion may arise from the answer.

With the calculator functions, any one of the functions N, I/Y, PV, or FV can be found from the others. How this is done is illustrated in the next example, which uses some previous problems.

The calculator assumes each problem has a cash outflow (entered as a negative) and a cash inflow (entered as a positive).  For simplicity, we will always show PV as positive, and FV as negative.

Example 4.7.3

You borrow $1,000 and agree to repay the loan with a single payment in 2 years. How much should you pay if interest is charged at 8% compounded quarterly?

To look at values entered in your calculator, just press [RCL] and then the value you want to check, e.g., [RCL] [N] should show 8.

Example 4.7.4

If an invested $8,000 results in a future value of $8,998.91 in nine months, what is the interest rate compounded quarterly?

You have:

Answer: 16% compounded quarterly.

Alternatively, you could solve the algebra problem:

[latex]$8,000(1+\frac{j_m}{4})^3=$8,998.91[/latex]

Which simplifies to:

[latex]j_m=4\left(\sqrt[3]{(\frac{FV}{PV})-1)}\right)=4\left(( \frac{FV}{PV})^{1/3}-1\right)[/latex]

But this is a much tougher problem!

Example 4.7.5

If $150,000 is invested at 12% compounded monthly and results in a future value of $169,023.75, for how long must it have been invested?

Answer:  11.9999973 or 12 months.

Alternatively, we could solve the algebra problem:

[latex]$150,000\left(1+\frac{0.12}{12}\right)^n=$169,023.75[/latex]

Which simplifies, using logarithms to:

[latex]n=\log_{1.01} \left(\frac{$169,023.75}{$150,000}\right)[/latex]

In general, the calculator is a very good option – you do not need to use logarithms, and can solve much faster.

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