Answer:
(1.2075)
Explanation:
Lets assume we are increasing a price on a $100 item to help visualize the steps.
The two steps of 5% and then 15% can each be expressed as:
5%: (1+0.05) [The 1 represents the fact that the final cost is full price (1) plus 5%(0.05)]
15% (1+0.15) [Same explanation, but now with 0.15 for 15%]
We can apply these factors individually:
Assume a base of $100:
5% increase would make it $105 [$100*(1.05)=$105]
15% increase: On top of the 5%, we would go to: $105*(1.15) = $120.75
Or we can use a single multiplier.
If we look at the steps from above, we see that the algebra consisted of taking the origianl price ($100) and multiplying it twice: once with (1+0.05) and once with (1+1.15). Write this in the form of an equation:
($100)*(1+0.05)*(1+0.15) = $120.75
Let's multiply (1+0.05)*(1+0.15)
= (1.2075)
We can use this single factor (multiplier) to find the correct/same value as before:
(1.2075)($100) = $120.75