sales of computer increased by 5% per year over a 7 year period. by what total percent did sales of computers increase during this time period. round the answer correct to one decimal place
(1.05^7 - 1) * 100%
To calculate the total percent increase in sales of computers over a 7-year period, we need to calculate the cumulative increase in each year.
Given that the sales of computers increased by 5% per year, the increase in the first year would be 5% of the initial sales. In the second year, the increase would be 5% of the sales from the first year, and so on.
To calculate the cumulative increase, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = final amount (sales after 7 years)
P = initial amount (sales at the beginning)
r = annual interest rate (5% = 0.05)
n = number of times the interest is compounded per year (assuming once per year)
t = number of years
In this case, we have:
A = P(1 + 0.05/1)^(1*7)
Since the initial sales amount can be assumed to be 100% or 1 in decimal form, we can calculate the final amount (A) as:
A = 1(1 + 0.05)^7
A = 1.05^7
A ≈ 1.4026
The final amount represents the total percent increase in sales over the 7-year period compared to the initial sales amount.
To determine the percent increase, we subtract the initial amount (1) from the final amount (1.4026), divide by the initial amount, and multiply by 100.
Percent Increase = [(A - P) / P] * 100
= [(1.4026 - 1) / 1] * 100
= 0.4026 * 100
≈ 40.26%
Therefore, the sales of computers increased by approximately 40.26% during this 7-year period.