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Financial Knowledge Assessment: Q10A

10.  Suppose you owe $1,000 on a loan and the interest rate you are charged is 20% per year compounding annually.  If you didn’t pay anything off, at this interest rate, during what time frame would the amount you owe have doubled?

  • A.  Between 0 and 2 years.
  • B.  Between 2 and 4 years.
  • C.  Between 4 and 6 years.
  • D.  Between 6 and 8 years.

Explanation:  The correct answer is “B. Between 2 and 4 years.”  You would have answered this question correctly if you understand the concept of compounding interest.  To explain, compounding interest is additional interest that you owe or earn off of the interest that had been accrued from a previous period.  In the context of this question, after the first year of not paying you would owe $1200.  To find this answer you would multiply $1000 by 1.20. 1.20 is what is known as the factor, and to find the factor you simply add 20% (.20) and 1 to make 1.20.  To find the factor regardless of interest rate, use this formula: , where  is the factor and is  the interest rate.  If you chose to forgo payments for another year, you would multiply $1200 by 1.20 to get $1440.  Notice the additional $40; this is the direct result of compounding interest.  If you keep doing the math you would notice that after 3 years, the amount you owe would be $1728 and after 4 years you would owe $2074.  Because the amount at the end of 4 years has exceeded $2000, you can determine that the time during which your owed amount doubled was between 2 and 4 years.  Additionally, there is a general principal in finance called the “rule of 72” which states that if you divide the interest rate expresses as a whole number.  The math would simply be 72/20 which is 3.6. 3.6 is the approximate number of periods that it would take for the amount you owe to double.

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