Phillippe invested $1,000 ten years ago and expected to have $1,800 today He has neither added nor withdrawn any money since his initial investment. All interest was reinvested and compounded annually. As it turns out, he only has $1,680 in his account today. Which one of the following must be true?
A) He earned simple interest rather than compound interest.
B) He earned a lower interest rate than he expected.
C) He did not earn any interest on interest as he expected.
D) He ignored the Rule of 72 which caused his account to decrease in value.
E) The future value interest factor turned out to be higher than he expected.

Question

Quizplus · Accepted Answer

If Phillippe earned compound interest at the expected rate, he should have $1,800 in his account today. The fact that he only has $1,680 means that he earned a lower interest rate than he expected. Simple interest, answer A, would result in an even lower value than $1,680. Answer C is incorrect because the reinvestment of interest is the definition of compound interest. Answer D is irrelevant since the Rule of 72 is a method for estimating the time it takes an investment to double, not for calculating the actual value of an investment. Answer E is also irrelevant because the future value interest factor is just a tool to calculate the future value of an investment based on its interest rate, time, and compounding frequency, but it does not affect the actual performance of the investment.

Phillippe Invested $1,000 Ten Years Ago and Expected to Have