Calculate the compound interest on $5000 at a rate of 6% per annum for 4 years.

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Question: Calculate the compound interest on $5000 at a rate of 6% per annum for 4 years.

Options:

Correct Answer: $1272.48

Solution:

Compound Interest = P(1 + r/n)^(nt) - P = 5000(1 + 0.06/1)^(1*4) - 5000 = 5000(1.262477) - 5000 = 1272.48

Calculate the compound interest on $5000 at a rate of 6% per annum for 4 years.

Calculate the compound interest on $5000 at a rate of 6% per annum for 4 years.

Step 1: Identify the principal amount (P), which is $5000.
Step 2: Identify the annual interest rate (r), which is 6%. Convert this to decimal form by dividing by 100: 6% = 0.06.
Step 3: Identify the number of times interest is compounded per year (n). Since it's compounded annually, n = 1.
Step 4: Identify the number of years (t), which is 4 years.
Step 5: Use the compound interest formula: A = P(1 + r/n)^(nt).
Step 6: Substitute the values into the formula: A = 5000(1 + 0.06/1)^(1*4).
Step 7: Simplify inside the parentheses: A = 5000(1 + 0.06)^4.
Step 8: Calculate (1 + 0.06) = 1.06.
Step 9: Raise 1.06 to the power of 4: 1.06^4 = 1.262477.
Step 10: Multiply by the principal: A = 5000 * 1.262477 = 6312.385.
Step 11: Calculate the compound interest by subtracting the principal from the total amount: Compound Interest = A - P = 6312.385 - 5000.
Step 12: The compound interest is $1312.385.

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).
Rate and Time – Recognizing the importance of the interest rate and the time period in calculating compound interest.