A man retires at age 50 with $605,000 in savings. He spends his savings at a steady rate, and after 6 years of retirement, he has spent $300

Question

A man retires at age 50 with $605,000 in savings. He spends his savings at a steady rate, and after 6 years of retirement, he has spent $300,000. Write an equation for the amount the man has in savings. When will he have $100,000 in savings?

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    2021-09-06T02:00:37+00:00

    Since it states that he “spends his savings at a steady rate,” we can assume this is a linear equation.

    What we know is that he started with $605,000 and after 6 years, he used $300,000. So, we just subtract what he had originally by what he used and get $305,000. We can now make the equation as follows:

    300,000=6x, where x is the amount of money he spent in one year. This equation simplifies to x=50,000, which is the amount of money he spent in one year.

    Since the question asks us to tell how long it will take him to reach $100,000 in savings, we can make the equation using previous value we have found:

    100,000=305,000-50,000x, where x is the number of years passed.

    So, this equation solves to -205,000=-50,000x, or x=4.1

    I’m not sure how you want to express your answer, but it took him 4.1 years on top of the 6 years already passed to reach $100,000. This mean 10.1 years in total.

    Hope this helps!

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