What will be the compound interest on an amount of $2000 at an annual interest rate of 5% for 3 years?

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Q: What will be the compound interest on an amount of $2000 at an annual interest rate of 5% for 3 years?

Solution: Compound Interest = P(1 + r/n)^(nt) - P = 2000(1 + 0.05/1)^(1*3) - 2000 = 2000(1.157625) - 2000 = 315.25

Steps: 11

Step 1: Identify the principal amount (P), which is $2000.
Step 2: Identify the annual interest rate (r), which is 5% or 0.05 in decimal form.
Step 3: Identify the number of times interest is compounded per year (n). Here, it is 1 (annually).
Step 4: Identify the number of years (t), which is 3 years.
Step 5: Use the compound interest formula: Compound Interest = P(1 + r/n)^(nt) - P.
Step 6: Substitute the values into the formula: Compound Interest = 2000(1 + 0.05/1)^(1*3) - 2000.
Step 7: Calculate (1 + 0.05/1) = 1.05.
Step 8: Calculate (1.05)^(1*3) = (1.05)^3 = 1.157625.
Step 9: Multiply by the principal: 2000 * 1.157625 = 2315.25.
Step 10: Subtract the principal from this amount: 2315.25 - 2000 = 315.25.
Step 11: The compound interest is $315.25.