Question

In a company's first year in operation, it made an annual profit of $127,000. The profit of the company increased at a constant 29% per year each year. How much total profit would the company make over the course of its first 28 years of operation, to the nearest whole number?​

Answer 1

The total profit a company makes over 28 years with a 29% annual increase is calculated using the compound interest formula. The first year's profit is $127,000, and for each year up to the 28th, the profit is calculated and all yearly profits are summed to obtain the total profit.

Step-by-step explanation:

To calculate the total profit a company makes over 28 years with an annual increase of 29%, we use the formula for compound interest. The compound interest formula, which is used to calculate the future value of an investment earning interest compounded at a regular interval, is given by P(1 + r)^n, where P is the principal amount (initial profit), r is the annual interest rate (rate of profit increase), and n is the number of periods (number of years).

In the given situation, the company's first-year profit is $127,000, and it increases at a constant 29% each year. Hence, for each of the 28 years, we calculate the profit for that year by applying the formula as follows: 127,000(1 + 0.29)^n, where n will take values from 1 to 28.

The total profit over the 28 years will be the sum of the individual yearly profits. This requires calculating the value for each year and then summing them up to obtain the total.