Question

Yoda invested $1,000 ten years ago and expected to have $1,800 today He has neither added nor withdrawn any money since his initial investment.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.

Answer 1

Yoda likely earned a lower interest rate than he expected, as compound interest can significantly affect investment outcomes over time. His ending balance was less than anticipated because a reduced rate decreases the total amount compounded annually.

Step-by-step explanation:

Understanding the Discrepancy in Yoda's Investment Returns

Based on the scenario where Yoda invested $1,000 and expected to have $1,800 after ten years but ended up with only $1,680, it is clear that one assumption made at the beginning of his investment period did not hold true. Given that there were no withdrawals and all interest was reinvested, the most likely explanation for why Yoda has less money than he expected is that he earned a lower interest rate than expected (Option B). This can be attributed to the fact that compound interest has a significant impact on investment growth, as seen in the example where a $3,000 investment at a 7% annual rate compounds to $44,923 over 40 years. Therefore, a lower interest rate would have a downward effect on the end value of the investment, resulting in less than the anticipated amount.