When inflation causes the price of an item to increase the new cost C and the original cost c are related by the formula C=c(1+r)^n, where r is the rate of inflation per year as a decimal and n is the number of years. What would be the price of a $4.99 item after six months of 5% inflation?
C = 4.99(1+.05)^1/2
Well, let's calculate that using some clown math, shall we? First, we need to convert six months into a decimal form of a year. So, 6 months is half a year, which is 0.5.
Now, the rate of inflation is 5%, so we convert that to 0.05.
To find the price after six months, we use the formula C = c(1 + r)^n, where c is the original cost and n is the number of years.
Plugging in the values, we have C = $4.99(1 + 0.05)^0.5.
So, let the clown math begin!
The circus ring spins, the confetti flies... and after some clown magic, the price of that $4.99 item after six months of 5% inflation is approximately $5.13.
Remember, this is just a silly estimation, so don't take it too seriously!
To find the new price of the item after six months of 5% inflation, we need to use the formula C=c(1+r)^n, where:
- c = original cost ($4.99)
- r = rate of inflation per year (5% = 0.05)
- n = number of years (6 months = 0.5 year)
Plugging in the values into the formula, we have:
C = $4.99 * (1 + 0.05)^(0.5)
Simplifying the expression inside the parentheses, we get:
C = $4.99 * (1.05)^(0.5)
Calculating the value inside the parentheses:
C = $4.99 * 1.0247
Multiplying the original cost by the calculated value, we get:
C ≈ $5.15
Therefore, the price of the item after six months of 5% inflation would be approximately $5.15.
To find the price of a $4.99 item after six months of 5% inflation, we can use the formula C = c(1 + r)^n, where:
- C is the new cost
- c is the original cost
- r is the rate of inflation per year as a decimal
- n is the number of years
First, let's convert the inflation rate from a yearly rate to a six-month rate. Since there are 12 months in a year, six months is half a year. Therefore, the inflation rate for six months would be half of the yearly rate.
Given that the yearly inflation rate is 5%, the inflation rate for six months would be 5% / 2 = 2.5% (expressed as a decimal, which is 0.025).
Now, we have the following values:
- c = $4.99 (original cost)
- r = 0.025 (inflation rate for six months)
- n = 0.5 (number of years, equivalent to six months)
Plugging in these values into the formula, we get:
C = $4.99 * (1 + 0.025)^0.5
To calculate this, raise (1 + 0.025) to the power of 0.5 (since we have a square root of half a year) and then multiply the result by $4.99.
Using a calculator or a spreadsheet program, we find that:
C ≈ $5.0227
Therefore, the price of a $4.99 item after six months of 5% inflation would be approximately $5.0227.