A sum of €5,000 is invested in an eight-year government bond with an annual equivalent rate (AER) of 6% - Leaving Cert Mathematics - Question 2 - 2012

To determine the AER for the second investment bond, we note that it gives 20% interest after 8 years. We set the future value of the investment as:

$1.2P = P \left(1 + \frac{i}{100}\right)^8$

Dividing both sides by $P$ gives:

$1.2 = \left(1 + \frac{i}{100}\right)^8$

Next, we take the eighth root of both sides:

$1 + \frac{i}{100} = (1.2)^{\frac{1}{8}}$

Calculating the right side:

$1 + \frac{i}{100} \approx \sqrt[8]{1.2} \approx 1.022682$

Now, isolating $i$:

$\frac{i}{100} \approx 1.022682 - 1 \approx 0.022682$ $i \approx 2.2682$

Thus, the equivalent AER for this bond is approximately: $\text{AER} \approx 2.305\% \text{ (correct to three decimal places)}.$