If the compound interest on an amount for 2 years is $200 at a rate of 10%, what

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Question: If the compound interest on an amount for 2 years is $200 at a rate of 10%, what is the principal?

Options:

Correct Answer: $1000

Solution:

Using the formula for compound interest, P = A / (1 + r)^n. Here, A = 200 + P, r = 0.1, n = 2.

If the compound interest on an amount for 2 years is $200 at a rate of 10%, what is the principal?

If the compound interest on an amount for 2 years is $200 at a rate of 10%, what is the principal?

Step 1: Understand that the compound interest formula is A = P(1 + r)^n, where A is the total amount after interest, P is the principal amount, r is the interest rate, and n is the number of years.
Step 2: We know the compound interest for 2 years is $200, so we can express A as A = P + 200.
Step 3: The interest rate is given as 10%, which can be written as a decimal: r = 0.1.
Step 4: The number of years is given as n = 2.
Step 5: Substitute A in the compound interest formula: P + 200 = P(1 + 0.1)^2.
Step 6: Calculate (1 + 0.1)^2, which is (1.1)^2 = 1.21.
Step 7: Now the equation is P + 200 = P * 1.21.
Step 8: Rearrange the equation to isolate P: P * 1.21 - P = 200.
Step 9: Factor out P: P(1.21 - 1) = 200.
Step 10: Simplify: P(0.21) = 200.
Step 11: Divide both sides by 0.21 to find P: P = 200 / 0.21.
Step 12: Calculate P: P = approximately 952.38.

Compound Interest – Understanding how compound interest accumulates over time and how to calculate the principal amount from the total interest earned.
Interest Rate and Time Period – Recognizing the relationship between the interest rate, time period, and the amount of interest accrued.
Formula Application – Applying the correct formula for compound interest to derive the principal amount.