Jenny Franklin estimates that as a result of completing her master’s degree, she will earn $7,000 a year more for the next 40 years.
a. What would be the total amount of these additional earnings?
b. What would be the future value of these additional earnings based on an annual interest rate of 6 percent?
Solution:
a. $7,000 40 = $280,000
b. $7,000 154.762 = $1,083,334
To find the total amount of these additional earnings, you need to multiply the increase in salary per year by the number of years.
a. To calculate the total amount of additional earnings:
Additional earnings per year = $7,000
Number of years = 40
Total additional earnings = Additional earnings per year × Number of years
Total additional earnings = $7,000 × 40
Total additional earnings = $280,000
Therefore, the total amount of these additional earnings over 40 years would be $280,000.
b. To calculate the future value of these additional earnings based on an annual interest rate of 6 percent, you can use the formula for the future value of a series of payments:
Future Value = P × [(1 + r)^n - 1] / r
Where:
P = Payment per period ($7,000)
r = Interest rate per period (6% or 0.06)
n = Number of periods (40 years)
Future Value = $7,000 × [(1 + 0.06)^40 - 1] / 0.06
Using a calculator or spreadsheet software, you can solve this equation to find the future value of these additional earnings.
Future Value = $7,000 × [5.7435 - 1] / 0.06
Future Value = $7,000 × 4.7435 / 0.06
Future Value = $548,870.83 (rounded to the nearest cent)
Therefore, the future value of these additional earnings based on an annual interest rate of 6 percent would be approximately $548,870.83.