If a sum of money grows to $1200 in 2 years at a compound interest rate of 10% p

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Question: If a sum of money grows to $1200 in 2 years at a compound interest rate of 10% per annum, what was the principal amount?

Options:

Correct Answer: $1000

Solution:

Using A = P(1 + r)^t, we have 1200 = P(1.21). Thus, P = 1200 / 1.21 = 991.74, rounded to $1000.

If a sum of money grows to $1200 in 2 years at a compound interest rate of 10% per annum, what was the principal amount?

If a sum of money grows to $1200 in 2 years at a compound interest rate of 10% per annum, what was the principal amount?

Step 1: Understand the formula for compound interest, which is A = P(1 + r)^t.
Step 2: Identify the values given in the problem: A (the amount after interest) is $1200, r (the interest rate) is 10% or 0.10, and t (the time in years) is 2.
Step 3: Convert the interest rate to a decimal by adding 1 to r: 1 + 0.10 = 1.10.
Step 4: Calculate (1 + r)^t: (1.10)^2 = 1.10 * 1.10 = 1.21.
Step 5: Substitute the values into the formula: 1200 = P * 1.21.
Step 6: Solve for P (the principal amount) by dividing both sides by 1.21: P = 1200 / 1.21.
Step 7: Calculate the value: P = 991.74.
Step 8: Round the principal amount to the nearest dollar: $991.74 rounds to $1000.

Compound Interest – Understanding how compound interest works and how to apply the formula A = P(1 + r)^t to find the principal amount.
Exponential Growth – Recognizing that the growth of money over time with compound interest is exponential rather than linear.