A sum of money invested at compound interest becomes $1500 in 2 years and $1800

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Question: A sum of money invested at compound interest becomes $1500 in 2 years and $1800 in 3 years. What is the rate of interest?

Options:

Correct Answer: 12%

Solution:

The interest for the third year is $300 (1800 - 1500). The principal for the second year is $1500, so the rate is (300/1500) * 100 = 20%.

A sum of money invested at compound interest becomes $1500 in 2 years and $1800 in 3 years. What is the rate of interest?

A sum of money invested at compound interest becomes $1500 in 2 years and $1800 in 3 years. What is the rate of interest?

Step 1: Understand that the amount of money grows due to compound interest.
Step 2: Note that the amount after 2 years is $1500 and after 3 years is $1800.
Step 3: Calculate the interest earned in the third year by subtracting the amount after 2 years from the amount after 3 years: $1800 - $1500 = $300.
Step 4: Recognize that the principal amount at the beginning of the second year is $1500.
Step 5: To find the rate of interest, use the formula: Rate = (Interest / Principal) * 100.
Step 6: Substitute the values into the formula: Rate = (300 / 1500) * 100.
Step 7: Calculate the rate: (300 / 1500) = 0.2, then multiply by 100 to get 20%.
Step 8: Conclude that the rate of interest is 20%.

Compound Interest – Understanding how compound interest works, including the calculation of interest over multiple periods.
Rate of Interest Calculation – Calculating the rate of interest based on the difference in amounts over specific time periods.