There are a few ways to solve the problem and determine how long it will take to double your money at a 6% compound interest. You could create a computer spreadsheet, solve by hand or use the Rule of 72 . The problem says that interest is compounded weekly, but...
There are a few ways to solve the problem and determine how long it will take to double your money at a 6% compound interest. You could create a computer spreadsheet, solve by hand or use the Rule of 72. The problem says that interest is compounded weekly, but keep in mind that the 6% interest rate is the annualized interest rate.
To solve this problem, you could create a spreadsheet and use the beginning balance in the account as your starting point. To keep it simple, use $100. The interest rate is 6%. Keep in mind that the question is about compounded interest, which means that you will receive interest on top of the interest income you earned in prior years.
Once you have set up your spreadsheet, you can multiply the $100 starting balance by 6%, which yields $6.00. Thus, a 6% interest rate on principle of $100 would produce $6.00 in interest income. This means that at the end of Year 1, you would have a new balance of $106 in your account. You then do the same thing on the new balance. Specifically,
$106 x 6% equals $6.36.
When you add $6.36 to the $106 balance you had at the end of Year 1, you see that you have $112.36 at the end of Year 2.
You can continue repeating this process until the money doubles or reaches about $200. In this case, you will double your money by Year 12, when the balance reaches $201.22. You could also do this problem by hand, repeating the step for each year and writing the year-end balance on your manual spreadsheet.
There is also a simpler way to approach the problem. You could use the Rule of 72, which states that to determine the number of years it will take to double your money, you divide the interest rate into 72. In this case:
72 divided by 6 equals 12.
The answer is the same using all three methods.