Question

James started saving money every week from his paycheck into his savings account. The table below shows the linear relationship between the number of weeks that passed and the total amount in his savings account.

Answer 1

James is using compound interest to grow his savings over time, underlining the significance of starting to save early to leverage the returns. Even without additional deposits, a one-time investment can significantly increase due to compound interest, contributing to financial stability at retirement.

Step-by-step explanation:

When James begins saving from his paycheck weekly, he's utilizing the concept of compound interest to grow his savings over time. By starting early, as in the hypothetical scenario where someone saves $3,000 at age 25, they could end up with $44,923 after 40 years, assuming a 7% real annual rate of return.

Such growth is due to the money not only earning interest on the initial amount but also on the accumulated interest from previous periods. Regularly saving a fixed amount amplifies the effect of compound interest, potentially creating a substantial sum by the time of retirement.

While it may not lead to wealth comparable to Bill Gates, it pushes one towards the top economic percentages of households. Understanding and applying compound interest can be highly beneficial for long-term financial health and stability.

Answer 2

To find the total amount in James's savings account after a certain number of weeks, you can use the formula y = mx + b, where y is the total amount, x is the number of weeks, m is the slope, and b is the y-intercept.

Step-by-step explanation:

The table represents a linear relationship between the number of weeks and the total amount in James's savings account.

To find the amount in his savings account after a certain number of weeks, you can use the formula

y = mx + b,

where y is the total amount, x is the number of weeks, m is the slope, and b is the y-intercept.

The slope represents the rate at which the money is being added to the account each week, and the y-intercept represents the initial amount in the account.

By finding the values of m and b from the table, you can determine the equation of the line and calculate the total amount for any given number of weeks.