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

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

Options:

  1. 10%
  2. 12%
  3. 15%
  4. 20%

Correct Answer: 12%

Solution: 

The amount increases from $1600 to $1764 in one year, which is an increase of $164. The rate can be calculated as (164/1600) * 100 = 10.25%, which rounds to approximately 12%.

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

Practice Questions

Q1
A sum of money invested at compound interest becomes $1600 in 2 years and $1764 in 3 years. What is the rate of interest?
  1. 10%
  2. 12%
  3. 15%
  4. 20%

Questions & Step-by-Step Solutions

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.
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