Question

An amount was invested at % r per quarter. What value of rwill ensure that accumulated amount at the end of one year is 1.5 times more than amount invested? Correct to 2 decimal places

Answer 1

42.67%

Explanation:

The annual growth factor for interest at annual rate r compounded quarterly is ...

(1 +r/4)^4

You want that value to be 1.5:

1.5 = (1 +r/4)^4

1.5^(1/4) = 1 +r/4

(1.5^(1/4) -1) = r/4

4(1.5^(1/4) -1) = r ≈ 0.426728

The rate r must be about 42.67%.

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Comment on the wording

We interpreted the problem to mean the end-of-year amount is 1.5 times the beginning-of-year amount. That is, it is "1.5 times the amount invested."

The word "more" is typically used when addition is involved. For example, "25% more" means 25% of the original is added to the original. We occasionally see "more" where "x times more" is intended to mean "x times", rather than "x times the amount, added to the original amount."