Question 5.S-TP.3: Calculating Rates of Return You’ve been offered an investmen...
Calculating Rates of Return You’ve been offered an investment that will double your money in 10 years. What rate of return are you being offered? Check your answer using the Rule of 72.
Suppose you invest $1,000. You will have $2,000 in 10 years with this investment.
So, $1,000 is the amount you have today, or the present value, and $2,000 is the amount you will have in 10 years, or the future value. From the basic present value equation, we have:
$2,000 = $1,000 × (1+r)^{10}
2 = (1+r)^{10}
From here, we need to solve for r , the unknown rate. As shown in the chapter, there are several different ways to do this. We will take the 10th root of 2 (by raising 2 to the power of 1/10):
2^{(1/10)} = 1 + r
1.0718 = 1 + r
r = 7.18%
Using the Rule of 72, we have 72/t = r %, or 72/10 = 7.2%; so, our answer looks good (remember that the Rule of 72 is only an approximation).