Question

8.36 Polly the Penguin invested $250 in the Antarctic stock market. During the first year her investment suffered a 15% loss, but during the second year the remaining investment showed a 20% gain. Over the two-year period, what was the percent loss or gain in Polly's investment?

Answer 1

5% gain

Step-by-step explanation: mental math

Answer 2

The percentage gain in Polly's investment over the two year period will be 2%.

Explanation:

Given:

- Polly the Penguin invested $250 in the Antarctic stock market.

- During the first year her investment suffered a 15% loss, but during the second year the remaining investment showed a 20% gain. Over the two-year period.

To Find:

- The percent loss or gain in Polly's investment.

The formula used to calculate percentage is: (value/totalvalue) x100%

- First, we determine the loss suffered by multiplying the loss percentage with the investment amount. Then, we get the amount after the loss is calculated. Then, we calculate the gain by multiplying the gain percentage with the previous amount to get the net amount in the second year.

Step 1 of 2

- The 15% loss in the first year on the investment amount $250 can be calculated as

`$$\begin{aligned}&=250-15 \% \text { of } 250 \\&=250-(15)/(100) * 250 \\&=250-(3)/(20) * 250 \\&=250-(750)/(20) \\&=250-37.5 \\&=\$ 212.50\end{aligned}$$`

Step 2 of 2

- The 20% gain in the second year can be calculated as

`$$\begin{aligned}&=212.50+20 \% \text { of } 212.50 \\&=212.50+(20)/(100) * 212.50 \\&=212.50+42.50 \\&=\$ 255\end{aligned}$$`

- Here, we can observe that the total profits increased by $5 from the initial investment of $250. This means that 1% gain is equal to $2.50. So, 2% gains mean $5.