A loan of $2000 is taken at a compound interest rate of 6% per annum. What will

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Question: A loan of $2000 is taken at a compound interest rate of 6% per annum. What will be the amount after 2 years?

Options:

Correct Answer: $2240

Solution:

Amount = Principal * (1 + Rate)^Time = 2000 * (1 + 0.06)^2 = 2000 * 1.1236 = $2247.20.

A loan of $2000 is taken at a compound interest rate of 6% per annum. What will be the amount after 2 years?

A loan of $2000 is taken at a compound interest rate of 6% per annum. What will be the amount after 2 years?

Step 1: Identify the principal amount (the initial loan). In this case, it is $2000.
Step 2: Identify the annual interest rate. Here, it is 6%, which can be written as 0.06 in decimal form.
Step 3: Identify the time period for which the loan is taken. In this case, it is 2 years.
Step 4: Use the compound interest formula: Amount = Principal * (1 + Rate)^Time.
Step 5: Substitute the values into the formula: Amount = 2000 * (1 + 0.06)^2.
Step 6: Calculate (1 + 0.06) which equals 1.06.
Step 7: Raise 1.06 to the power of 2: 1.06^2 = 1.1236.
Step 8: Multiply the principal amount by the result: 2000 * 1.1236 = 2247.20.
Step 9: The final amount after 2 years is $2247.20.

Compound Interest – The interest calculated on the initial principal and also on the accumulated interest from previous periods.
Exponential Growth – Understanding how the amount grows exponentially over time due to compounding.
Formula Application – Correctly applying the compound interest formula: Amount = Principal * (1 + Rate)^Time.