Question

If prices of gold decrease at a monthly rate of 0.3%, by what percentage do they decrease in a year? Round to the nearest tenth of a percent.

a. 4.4%
b. 3.5%
c. 3.7%
d. 3.6%

Answer 1

To calculate the annual percentage decrease with a monthly rate of 0.3%, compound the rate over 12 months. The resulting annual percentage decrease is approximately 3.592%, which rounds to 3.6%.

Step-by-step explanation:

To calculate the annual percentage decrease if the gold prices decrease at a monthly rate of 0.3%, we need to compound the monthly decrease over 12 months. The formula to calculate the compounded rate is (1 + r)ⁿ, where r is the monthly rate and n is the number of periods (months in this case).

Let's plug in the values:

(1 - 0.003)¹² = (0.997)¹²

Using a calculator, we find that (0.997)¹² ≈ 0.96408.

The annual decrease is therefore 1 - 0.96408 = 0.03592, or 3.592%. When rounded to the nearest tenth of a percent, the annual percentage decrease in gold prices is 3.6%.

Therefore, the correct answer is d. 3.6%.