5.05 Comparing investment strategies

To select the most desirable investment strategy from a selection of different options, we will usually choose the option that returns the most interest. Recall that the interest is found by taking the difference between the final value and the initial principal amount of the investment.

Looking again at the formula for simple interest:

$FV=PV\left(1+rn\right)$FV=PV(1+rn)

and the formula for compound interest:

$FV=PV\left(1+r\right)^n$FV=PV(1+r)n

we can see that different investment strategies can be designed by changing any of the following variables: the present value ($PV$PV), the interest rate ($r$r), the compounding frequency, and/or the number of periods ($n$n).

If we only alter one variable, such as the present value, it is easy to see which of two investment strategies will return the most interest. Choosing between two strategies becomes more complex when we vary more than one of these variables.

Comparing simple interest investments

Consider the following investment strategies that use simple interest:

• Investment strategy 1: investing $\$100$$100 at $3.5%$3.5% p.a. for $5$5 years

• Investment strategy 2: investing $\$100$$100 at $4.7%$4.7% p.a. for $5$5 years

Which strategy should we choose in order to maximise the value of our investment?

Each strategy has the same present value and investment duration. The only difference is the interest rate. In this case we should expect that the investment strategy with the higher interest rate will create a higher return. Let's check this with some calculations

First let's determine the final value of investment strategy 1:

$FV$FV	$=$=	$PV\left(1+rn\right)$PV(1+rn)
	$=$=	$100\left(1+\frac{3.5}{100}\times5\right)$100(1+3.5100​×5)
	$=$=	$100\left(1+0.035\times5\right)$100(1+0.035×5)
	$=$=	$100\left(1+0.175\right)$100(1+0.175)
	$=$=	$100\times1.175$100×1.175
	$=$=	$117.5$117.5

So if we select investment 1, our $\$100$$100 will become $\$117.50$$117.50 in $5$5 years' time.

Using the same approach, we will find that investment 2 will turn $\$100$$100 into $\$123.50$$123.50 after $5$5 years. This means that investment 2 is the better option, because it will have the greater value after $5$5 years.

The final value of a simple interest investment varies linearly with the interest rate. This means that, all else being equal, a higher interest rate will yield a higher return on the investment.

Comparing compound interest investments

Compare the interest earned on these two investment strategies that use compound interest:

• Investment strategy 1: investing $\$450$$450 at $2.59%$2.59% p.a., compounded annually, for $7$7 years

• Investment strategy 2: investing $\$280$$280 at $4.73%$4.73% p.a., compounded monthly, for $6$6 years

These two strategies feature different initial investment amounts, different interest rates, different compounding frequencies and different investment periods. There is no quick way for us to know at a glance which will be worth the most, but we can determine each final value using the compound interest formula.

Investment 1 has an annual interest rate and annual compounding frequency, so we can use the compound interest formula and directly substitute the given values.

$FV$FV	$=$=	$PV\left(1+r\right)^n$PV(1+r)n
	$=$=	$450\left(1+\frac{2.59}{100}\right)^7$450(1+2.59100​)7
	$=$=	$450\left(1+0.0259\right)^7$450(1+0.0259)7
	$=$=	$450\times1.0259^7$450×1.02597
	$=$=	$538.20$538.20 (2 d.p.)

So using the first strategy we will have earned $538.20-450=\$88.20$538.20−450=$88.20 in interest over the $7$7 years.

Now for investment 2. We will first need to convert the annual interest rate to a monthly interest rate, and the investment period into a number of months.

$FV$FV	$=$=	$PV\left(1+r\right)^n$PV(1+r)n
	$=$=	$280\left(1+\frac{4.73}{100\times12}\right)^{6\times12}$280(1+4.73100×12​)6×12
	$=$=	$280\left(1+\frac{4.73}{1200}\right)^{72}$280(1+4.731200​)72
	$=$=	$371.68$371.68 (2 d.p.)

Using the second strategy we will have earned $371.68-280=\$91.68$371.68−280=$91.68 in interest over the $4$4 years.

Even though the initial investment amount and the investment period were lower, the second strategy yielded a greater amount of interest because it had a higher interest rate and a higher compounding frequency.

Always use the formula when comparing strategies that vary in more than one variable.

Practice questions

Question 1

Question 2