Martin invested $1,000 six years ago and expected to have $1,500 today. He has n

Question

Martin invested $1,000 six years ago and expected to have $1,500 today. He has not added or withdrawn any money from this account since his initial investment. All interest was reinvested in the account. As it turns out, Martin only has $1,520 in his account today. Which one of the following must be true? Martin earned simple interest rather than compound interest Martin earned a lower interest rate than he expected. Martin did not earn any interest on interest as he expected. Martin ignored the Rule of 72 which caused his account to decrease in value. Martin earned a higher interest rate than he expected.

Explanation / Answer

In this case Martin’s account balance today is $1,520. This is more than the expected amount of money of $1,500.

The only possible reason that Martin’s account has a greater balance than the expected amount is that “Martin earned a higher interest rate than he expected”.

Thus the answer is the last option.

Explanation through calculation:

Let the expected interest rate be i%. Thus 1000*(1+i)^6 = 1500

Or (1+i)^6 = 1.5

Or 1+I = 1.069913

Or I = 6.99%

Actual interest rate earned by Martin:

Let the actual interest rate be x%

Thus 1000*(1+x)^6 = 1520

Or (1+x)^6 = 1.52

Or 1+x = 1.07228

Or x = 7.23%

Clearly Martin earned a higher interest rate than expected.

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