Question

You are interviewing for a job and receive two offers for a five-year contract: A: \(\$ 40,000\) to start, with guaranteed annual increases of \(6 \%\) for the first 5 years B: \(\$ 44,000\) to start, with guaranteed annual increases of \(3 \%\) for the first 5 years Which offer is better if your goal is to be making as much as possible after 5 years? Which is better if your goal is to make as much money as possible over the contract (5 years)?

Short answer

A has a higher salary after 5 years. B has higher total earnings over 5 years.

Step-by-step solution

- Calculate the Salary After 5 Years for Option A

To find the salary after 5 years with annual increases, use the formula for compound interest: P = Principal Amount r = Annual Increase Rate n = Number of Years So, the salary after 5 years is given by: S_A = 40000 * (1 + 0.06)^5 Calculate this value: S_A = 40000 * (1.3382) S_A = 53,528

- Calculate the Salary After 5 Years for Option B

Similarly, use the compound interest formula to find the salary after 5 years for Option B: S_B = 44000 * (1 + 0.03)^5 Calculate this value: S_B = 44000 * (1.159274) S_B = 50,007

- Determine Which Offer Has a Higher Salary After 5 Years

Compare the results from Steps 1 and 2: S_A = 53,528 S_B = 50,007 Option A offers a higher salary after 5 years.

- Calculate the Total Earnings Over 5 Years for Option A

To find the total earnings over 5 years, sum the salaries for each year. For Option A: Year 1: 40,000 Year 2: 40,000 * (1 + 0.06) = 42,400 Year 3: 42,400 * (1 + 0.06) = 44,944 Year 4: 44,944 * (1 + 0.06) = 47,640 Year 5: 47,640 * (1 + 0.06) = 50,498 Total Earnings_A = 40,000 + 42,400 + 44,944 + 47,640 + 50,498 = 225,482

- Calculate the Total Earnings Over 5 Years for Option B

Similarly, sum the salaries for each year for Option B: Year 1: 44,000 Year 2: 44,000 * (1 + 0.03) = 45,320 Year 3: 45,320 * (1 + 0.03) = 46,680 Year 4: 46,680 * (1 + 0.03) = 48,080 Year 5: 48,080 * (1 + 0.03) = 49,522 Total Earnings_B = 44,000 + 45,320 + 46,680 + 48,080 + 49,522 = 233,602

- Determine Which Offer Has Higher Total Earnings Over 5 Years

Compare the total earnings from Steps 4 and 5: Total Earnings_A = 225,482 Total Earnings_B = 233,602 Option B offers higher total earnings over 5 years.

Key concepts

Salary Growth

When evaluating job offers, it's crucial to understand how salary growth works. Salary growth refers to the increase in your salary over time. Different companies might offer various rates of annual raises. To compare job offers, one must calculate the future salary based on these raises.

In the given scenario, we're comparing two job offers with different starting salaries and raise rates. This involves understanding the principle of compound interest since your salary increases by a certain percentage each year. Both offers guarantee annual raises, but at different rates (6% for Offer A and 3% for Offer B).

Annual Increase Rate

The annual increase rate, or raise rate, significantly impacts long-term salary outcomes. This rate indicates how much your salary will increase each year.

In our example, **Option A** offers a 6% annual increase, which quickly compounds over five years. Conversely, **Option B** offers a 3% annual increase, leading to smaller increments each year.

Calculating these increases involves the formula for compound interest:
S = P (1 + r)^n Where:

• P is the initial principal (starting salary)
• r is the annual increase rate (expressed as a decimal)
• n is the number of years

For Option A: S_A = 40000 (1 + 0.06)^5 calculated as: S_A = 40000 (1.3382) ≈ 53,528 Whereas for Option B: S_B = 44000 (1 + 0.03)^5 S_B = 44000 (1.159274) ≈ 50,007 Thus, we see that after 5 years, Option A will offer a higher salary.

Total Earnings Calculation

Total earnings over a period give you a complete picture of the financial benefits. Calculating total earnings involves summing up the annual salaries for each year.

For **Option A** over 5 years, the calculations are as follows:

• Year 1: 40,000
• Year 2: 40,000 * (1 + 0.06) = 42,400
• Year 3: 42,400 * (1 + 0.06) = 44,944
• Year 4: 44,944 * (1 + 0.06) = 47,640
• Year 5: 47,640 * (1 + 0.06) = 50,498
• Total: 225,482

For **Option B**, the calculations are:

• Year 1: 44,000
• Year 2: 44,000 * (1 + 0.03) = 45,320
• Year 3: 45,320 * (1 + 0.03) = 46,680
• Year 4: 46,680 * (1 + 0.03) = 48,080
• Year 5: 48,080 * (1 + 0.03) = 49,522
• Total: 233,602

In this example, **Option B** offers higher total earnings over 5 years. Thus, if your focus is monetary gain across the contract's duration rather than the highest year-5 salary, Option B is better.

Understanding the relationship between salary growth, the annual increase rate, and total earnings is vital for making informed career decisions.