Question

Jack has $500 in a bank account that will earn 3% interest every year. Diane has $100 in an investment account that will earn 12% every year. How many years will it take for Diane's account balance to overtake Jack’s?

Answer 1

20 years

Explanation:

A=500(1+.03)^20

$903

A=100(1+.12)^20

$964

It took her 20 years to overtake.

Answer 2

• Simple interest = Never
• Compound interest = 19 years and 4 months

Explanation:

Jack

• Initial amount = $500
• Interest rate = 3% = 0.03

Yearly interest = 0.03*500 = $15

Diane

• Initial amount = $100
• Interest rate = 12% = 0.12

Yearly interest = 0.12*100 = $12

Diane's initial amount and yearly interest amount are both less than of Jack's.

It means her balance will never overtake Jack's.

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It is not mentioned in the question but let's assume it is compound interest which is annually compounded.

Then after x years their balance will be:

Jack

• 500(1 + 0.03)^x = 500*1.03^x

Diane

• 100(1 + 0.12)^x = 100*1.12^x

Solve inequality below:

• 100*1.12^x ≥ 500*1.03^x
• (1.12/1.03)^x ≥ 5
• 1.087^x ≥ 5
• x log 1.087 ≥ log 5
• x ≥ log 5 / log 1.087
• x ≥ 19.29 years = 19 years and 4 months