Question

Suppose a doctor earns $40,000 during the first year of practice. suppose also that each succeeding year the salary increases 10%. what is the total of the doctor's salaries over the first 10 years?

Answer 1

The total of the doctor's salaries over the first 10 years is $637,600.

Step-by-step explanation:

To find the total of the doctor's salaries over the first 10 years, we can use the formula for compound interest. The doctor's salary increases by 10% each year, so we can think of it as a compounded interest problem. Starting with a salary of $40,000, we can calculate the salary for each year by multiplying the previous year's salary by 1.10. So, the salary for the second year would be $40,000 * 1.10, the salary for the third year would be $40,000 * 1.10 * 1.10, and so on.

This can be simplified using the geometric series formula: salary = first term * (1 - common ratio ^ number of terms) / (1 - common ratio). In this case, the first term is $40,000, the common ratio is 1.10, and the number of terms is 10.

Substituting these values into the formula, we get:

salary = $40,000 * (1 - 1.10^10) / (1 - 1.10) = $40,000 * (1 - 2.5940) / (-0.10) = $40,000 * (-1.5940) / (-0.10) = $40,000 * 15.940 = $637,600.

Answer 2

$94,427.89 , best of luck