A sum of money invested at compound interest becomes $1600 in 2 years and $1764

A sum of money invested at compound interest becomes $1600 in 2 years and $1764 in 3 years. What is the rate of interest?

A sum of money invested at compound interest becomes $1600 in 2 years and $1764 in 3 years. What is the rate of interest?

Step 1: Identify the amounts given. The amount after 2 years is $1600 and after 3 years is $1764.
Step 2: Calculate the increase in amount from year 2 to year 3. This is $1764 - $1600 = $164.
Step 3: The increase of $164 happens over 1 year (from year 2 to year 3).
Step 4: To find the rate of interest, divide the increase by the amount at the beginning of the year (which is $1600). So, calculate 164 / 1600.
Step 5: Calculate the result of 164 / 1600, which is 0.1025.
Step 6: To express this as a percentage, multiply by 100. So, 0.1025 * 100 = 10.25%.
Step 7: Round 10.25% to the nearest whole number, which is approximately 10%.

Compound Interest – Understanding how compound interest works and how to calculate the rate of interest based on the growth of an investment over time.
Percentage Calculation – Calculating the percentage increase in value to determine the interest rate.