Calculate the compound interest on $2000 for 2 years at an interest rate of 8% p

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Question: Calculate the compound interest on $2000 for 2 years at an interest rate of 8% per annum.

Options:

Correct Answer: $256

Solution:

Compound Interest = P(1 + r/n)^(nt) - P = 2000(1 + 0.08/1)^(1*2) - 2000 = 2000(1.1664) - 2000 = $256

Calculate the compound interest on $2000 for 2 years at an interest rate of 8% per annum.

Calculate the compound interest on $2000 for 2 years at an interest rate of 8% per annum.

Step 1: Identify the principal amount (P), which is $2000.
Step 2: Identify the annual interest rate (r), which is 8%. Convert this to decimal form by dividing by 100: 8% = 0.08.
Step 3: Identify the number of times interest is compounded per year (n). Since it is compounded annually, n = 1.
Step 4: Identify the number of years (t), which is 2 years.
Step 5: Use the compound interest formula: A = P(1 + r/n)^(nt).
Step 6: Substitute the values into the formula: A = 2000(1 + 0.08/1)^(1*2).
Step 7: Calculate the expression inside the parentheses: 1 + 0.08 = 1.08.
Step 8: Raise 1.08 to the power of (1*2) = 2: 1.08^2 = 1.1664.
Step 9: Multiply this result by the principal: 2000 * 1.1664 = 2332.8.
Step 10: To find the compound interest, subtract the principal from this amount: 2332.8 - 2000 = 332.8.
Step 11: The compound interest earned over 2 years is $332.8.

Compound Interest – The interest calculated on the initial principal, which also includes all the accumulated interest from previous periods.
Formula Application – Understanding and correctly applying the compound interest formula: A = P(1 + r/n)^(nt).
Interest Rate Conversion – Converting the annual interest rate into a decimal for calculations.