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A sum of money invested at compound interest grows to $1500 in 2 years and to $1
A sum of money invested at compound interest grows to $1500 in 2 years and to $1800 in 3 years. What is the rate of interest?
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Q1
A sum of money invested at compound interest grows to $1500 in 2 years and to $1800 in 3 years. What is the rate of interest?
10%
15%
20%
25%
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Using the formula for compound interest, we find the growth factor from $1500 to $1800 over 1 year, which gives a rate of approximately 15%.
Questions & Step-by-step Solutions
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Q
Q: A sum of money invested at compound interest grows to $1500 in 2 years and to $1800 in 3 years. What is the rate of interest?
Solution:
Using the formula for compound interest, we find the growth factor from $1500 to $1800 over 1 year, which gives a rate of approximately 15%.
Steps: 7
Show Steps
Step 1: Identify the amounts after 2 years and 3 years. We have $1500 after 2 years and $1800 after 3 years.
Step 2: Calculate the growth from year 2 to year 3. This is $1800 - $1500 = $300.
Step 3: The growth of $300 occurs over 1 year (from year 2 to year 3).
Step 4: To find the rate of interest, we use the formula: Rate = (Growth / Initial Amount) * 100%.
Step 5: The initial amount at the start of year 3 is $1500. So, Rate = ($300 / $1500) * 100%.
Step 6: Calculate the rate: Rate = 0.2 * 100% = 20%.
Step 7: Since this is the growth for one year, we can conclude that the rate of interest is approximately 20%.
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