Over the past 6 months, the price of a speaker has undergone many price increases and reductions. Originally the speaker was $430 and then it incurred a price reduction of 20%. 2 months later the price was increased by 20%. After another 2 months the price was then reduced by 15%, only to be increased by 20% 2 months following that.Find the price of the speaker at the end of the 6 months.Give your answer correct to the nearest cent.

Let's break this down:

1. The speaker originally costs $430.

2. It first incurred a price reduction of 20%. To find the new price, we multiply the original price by 20% (or 0.20) and subtract that from the original price.

   $430 * 0.20 =$86.

   $430 -$86 = $344.

   So, after the first price reduction, the speaker costs $344.

3. Two months later, the price was increased by 20%. To find the new price, we multiply the current price by 20% (or 0.20) and add that to the current price.

   $344 * 0.20 =$68.80.

   $344 +$68.80 = $412.80.

   So, after the price increase, the speaker costs $412.80.

4. After another two months, the price was reduced by 15%. To find the new price, we multiply the current price by 15% (or 0.15) and subtract that from the current price.

   $412.80 * 0.15 =$61.92.

   $412.80 -$61.92 = $350.88.

   So, after the second price reduction, the speaker costs $350.88.

5. Two months following that, the price was increased by 20%. To find the new price, we multiply the current price by 20% (or 0.20) and add that to the current price.

   $350.88 * 0.20 =$70.18.

   $350.88 +$70.18 = $421.06.

   So, after the second price increase, the speaker costs $421.06.

Therefore, at the end of the 6 months, the speaker costs $421.06.