Question

If your starting salary is $40,000 and you receive a 3% increase at the end of every year, what is the total amount, in dollars, you will earn over the first 16 years that you work?

Answer 1

To calculate the total earnings over 16 years with a starting salary of $40,000 and an annual 3% increase, apply the compound interest formula to each year's salary and cumulatively add them. This is similar to calculating compound interest on an initial investment, accounting for the yearly compounding factor.

Step-by-step explanation:

If the starting salary is $40,000 and there is a 3% increase each year, to calculate the total amount earned over the first 16 years, one must account for this yearly raise being compounded. This is a straightforward application of the formula used in calculating the future value in the case of compound interest. By treating each year's salary as a compounding amount, we can find the total salary over 16 years.

To find the salary at the end of each year, we would use the formula:
Salary = Principal × (1 + Rate)Number of years,
where the Principal is the initial amount ($40,000), the Rate is the annual increase (3% or 0.03), and the Number of years is how many years since the start (from 1 to 16).

For example, in the first year, the total salary is simply the starting salary, which is $40,000. In the second year, the salary would be $40,000 × (1 + 0.03) which equals $41,200. We repeat this calculation incrementally for 16 years and add all the annual totals to get the cumulative amount earned.

So, the step-by-step approach is:

1. Calculate the salary for each year by applying the above formula.
2. Repeat this for each of the 16 years, incrementing the Number of years by 1 each time.
3. Add all calculated annual salaries to find the total amount earned over the 16 years.

Using a spreadsheet or a calculator would make this work much more manageable, as it would automatically apply the formula for each year and sum the totals for you.