If the compound interest on a sum of money for 2 years at 10% per annum is $121,

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Question: If the compound interest on a sum of money for 2 years at 10% per annum is $121, what is the principal amount?

Options:

Correct Answer: $1000

Solution:

Using the formula for compound interest, A = P(1 + r/n)^(nt). Here, A = P + 121, r = 0.1, n = 1, t = 2. Solving gives P = 1000.

If the compound interest on a sum of money for 2 years at 10% per annum is $121, what is the principal amount?

If the compound interest on a sum of money for 2 years at 10% per annum is $121, what is the principal amount?

Step 1: Understand that the compound interest formula is A = P(1 + r/n)^(nt).
Step 2: Identify the variables: A is the total amount after interest, P is the principal amount (the initial sum of money), r is the interest rate (10% or 0.1), n is the number of times interest is compounded per year (1 for annually), and t is the number of years (2).
Step 3: Since the compound interest for 2 years is $121, we can express A as P + 121.
Step 4: Substitute the known values into the formula: A = P + 121, r = 0.1, n = 1, t = 2.
Step 5: Rewrite the formula: P + 121 = P(1 + 0.1/1)^(1*2).
Step 6: Simplify the right side: P + 121 = P(1 + 0.1)^2 = P(1.1)^2.
Step 7: Calculate (1.1)^2, which equals 1.21, so the equation becomes P + 121 = 1.21P.
Step 8: Rearrange the equation to isolate P: 121 = 1.21P - P.
Step 9: Simplify the equation: 121 = 0.21P.
Step 10: Solve for P by dividing both sides by 0.21: P = 121 / 0.21.
Step 11: Calculate P, which equals approximately 1000.

Compound Interest – Understanding how compound interest is calculated over multiple periods.
Principal Amount Calculation – Determining the initial amount of money based on the interest earned.
Interest Rate Application – Applying the correct interest rate to the principal over the specified time.