Financial Literacy: Compound Interest and the Rule of 72
Estimating growth, doubling time, and interest earned
Financial Literacy: Compound Interest and the Rule of 72
Estimating growth, doubling time, and interest earned
Financial Literacy - Grade 6-8
- 1
Maya deposits $200 in a savings account that earns 5% interest per year, compounded annually. How much money will she have after 1 year?
Find 5% of $200, then add it to the starting amount.
Maya will have $210.00 after 1 year because 5% of $200 is $10, and $200 plus $10 equals $210. - 2
Jalen invests $100 at 10% interest per year, compounded annually. Complete the amounts for the first 3 years: Year 0, Year 1, Year 2, and Year 3.
The amounts are Year 0: $100.00, Year 1: $110.00, Year 2: $121.00, and Year 3: $133.10. Each year, the amount is multiplied by 1.10. - 3
Use the Rule of 72 to estimate how many years it will take an investment to double if it earns 6% interest per year.
Rule of 72: 72 divided by the annual interest rate gives the approximate doubling time.
It will take about 12 years to double because 72 divided by 6 equals 12. - 4
Use the Rule of 72 to estimate how many years it will take money to double at 8% interest per year.
It will take about 9 years to double because 72 divided by 8 equals 9. - 5
A $500 investment doubles after about 12 years. Use the Rule of 72 to estimate the annual interest rate.
If you know the doubling time, divide 72 by the number of years.
The annual interest rate is about 6% because 72 divided by 12 equals 6. - 6
Which investment doubles faster: Investment A earns 4% interest per year, or Investment B earns 9% interest per year? Use the Rule of 72 to explain.
Investment B doubles faster. Investment A takes about 18 years because 72 divided by 4 equals 18, while Investment B takes about 8 years because 72 divided by 9 equals 8. - 7
Lena puts $300 in an account earning 4% interest per year, compounded annually. What is the account balance after 2 years?
Compound interest means the second year earns interest on the new balance, not just the starting amount.
The account balance after 2 years is $324.48. After 1 year, $300 multiplied by 1.04 is $312.00, and after 2 years, $312.00 multiplied by 1.04 is $324.48. - 8
An account starts with $1,000 and earns 7% interest per year. Use the Rule of 72 to estimate the balance after about 10 years.
The balance will be about $2,000 after about 10 years because 72 divided by 7 is about 10.3, so the money nearly doubles in that time. - 9
The graph shows two accounts that both start at $100. Account X earns simple interest, and Account Y earns compound interest. Which account has the curved line, and why?
Simple interest adds the same amount each year, while compound interest adds a growing amount each year.
Account Y has the curved line because compound interest grows faster over time as interest is added to both the original money and earlier interest. - 10
A savings account earns 3% interest per year, compounded annually. If the starting balance is $400, what is the balance after 1 year and after 2 years?
After 1 year, the balance is $412.00 because $400 multiplied by 1.03 equals $412.00. After 2 years, the balance is $424.36 because $412.00 multiplied by 1.03 equals $424.36. - 11
Use the Rule of 72 to match each interest rate with its approximate doubling time: 2%, 6%, 12% and 36 years, 12 years, 6 years.
Divide 72 by each interest rate.
The matches are 2% with 36 years, 6% with 12 years, and 12% with 6 years. Each match is found by dividing 72 by the interest rate. - 12
Noah wants his $250 to grow to about $500 in 8 years. Use the Rule of 72 to estimate the interest rate he would need.
Noah would need an interest rate of about 9% per year because 72 divided by 8 equals 9.