Question

An investor who was not as astute as he believed invested $281,000 into an account 6 years ago. Today, that account is worth $217,200. What was the annual rate of return on this account?

a) 3%
b) 4%
c) 5%
d) 6%

Answer 1

The annual rate of return on the investor's account was approximately -4.16%, which is closest to a 4% annual loss. To find this, we used the compound interest formula and solved for the rate, factoring in the decrease in account value over 6 years. The correct option is B.

Step-by-step explanation:

To calculate the annual rate of return, we need to use the formula for compound interest. However, in this case, the value of the account has decreased, which means the investor has experienced a negative return. We need to find the rate 'r' in the following equation that represents the decay of the original investment of $281,000 to $217,200 over 6 years:

Principal * (1 + r)^n = Final Amount

Where principal = $281,000, final amount = $217,200, and n = 6 (years). To find the annual rate of return (r), we rearrange the formula and solve for r:

($217,200 / $281,000) = (1 + r)^6

0.773024 = (1 + r)^6

We then take the 6th root of 0.773024 and subtract 1 to find r:

r ≈ (0.773024)^(1/6) - 1

r ≈ -0.0416 or -4.16%

Thus, the closest answer from the options provided is:

b) 4%