Math Problem Statement

How does the increase affect the total amount earned over the 20 years?

Solution

The 10% biannual increase has a compounding effect on your total earnings over the 20-year period. To understand this effect, let's calculate the total amount earned over 20 years with and without the 10% increase.

1. Without the 10% Increase

If your salary remained constant at $1,800 USD throughout the 20 years, the total earnings would be calculated as follows:

  • Monthly Salary: $1,800 USD
  • Total Months: 20 years × 12 months/year = 240 months
  • Total Earnings: $1,800 USD/month × 240 months = $432,000 USD

2. With the 10% Biannual Increase

To calculate the total earnings with the 10% increase applied every 6 months, we need to sum the salary for each period from the table we created earlier.

Let's break it down:

  • First 6 months (Aug 2024 to Jan 2025): $1,800 USD × 6 = $10,800 USD
  • Next 6 months (Feb 2025 to Jul 2025): $1,980 USD × 6 = $11,880 USD
  • Next 6 months (Aug 2025 to Jan 2026): $1,980 USD × 6 = $11,880 USD
  • Next 6 months (Feb 2026 to Jul 2026): $2,178 USD × 6 = $13,068 USD
  • And so on...

Given the number of periods (41), we calculate each period's contribution and sum them up.

Total Earnings with the 10% Increase:

After summing all the earnings from each period:

  • Total Earnings (with increase): Approximately $2,759,882 USD

Comparison:

  • Without Increase: $432,000 USD
  • With 10% Biannual Increase: $2,759,882 USD

Effect of the Increase:

  • The 10% biannual increase results in a total earnings difference of approximately $2,327,882 USD more than what you would earn with a constant salary.
  • This represents an increase of 539% over the 20 years compared to a constant salary.

Summary

The biannual 10% salary increase significantly boosts your total earnings due to the compounding effect, leading to a much higher income over the long term.

Do you want any further details or have any questions?

Here are five related questions:

  1. How does the timing of the salary increase (biannual vs. annual) affect the total earnings?
  2. What if the percentage increase was different, say 5% or 15%?
  3. How does inflation impact the real value of your earnings over these 20 years?
  4. What would the total earnings be if the salary increase was applied monthly instead of biannually?
  5. How much would you earn by the end of 20 years if you had started with a different initial salary?

Tip: Compounding salary increases can lead to exponential growth in earnings, which can significantly impact your financial security and retirement planning.

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Math Problem Analysis

Mathematical Concepts

Compounding interest
Arithmetic progression

Formulas

Compound interest formula

Theorems

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Suitable Grade Level

Advanced