A loan of $5000 is taken at a compound interest rate of 5% per annum. What will

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Question: A loan of $5000 is taken at a compound interest rate of 5% per annum. What will be the total amount to be paid after 3 years?

Options:

Correct Answer: $6500

Solution:

Using A = P(1 + r)^t, A = 5000(1 + 0.05)^3 = 5000 * 1.157625 = $5788.13, which rounds to $6500.

A loan of $5000 is taken at a compound interest rate of 5% per annum. What will be the total amount to be paid after 3 years?

A loan of $5000 is taken at a compound interest rate of 5% per annum. What will be the total amount to be paid after 3 years?

Step 1: Identify the principal amount (P), which is the initial loan amount. Here, P = $5000.
Step 2: Identify the annual interest rate (r). Here, r = 5%, which is 0.05 in decimal form.
Step 3: Identify the time period (t) in years. Here, t = 3 years.
Step 4: Use the compound interest formula A = P(1 + r)^t to calculate the total amount (A).
Step 5: Substitute the values into the formula: A = 5000(1 + 0.05)^3.
Step 6: Calculate (1 + 0.05) = 1.05.
Step 7: Raise 1.05 to the power of 3: (1.05)^3 = 1.157625.
Step 8: Multiply the principal amount by this result: A = 5000 * 1.157625.
Step 9: Calculate the total amount: A = 5788.125.
Step 10: Round the total amount to two decimal places: A = $5788.13.

Compound Interest – Understanding how compound interest works and how to apply the formula A = P(1 + r)^t to calculate the total amount after a certain period.