If the compound interest on a sum of money for 3 years at 12% per annum is $500,

₹0.0

Question: If the compound interest on a sum of money for 3 years at 12% per annum is $500, what is the principal amount?

Options:

Correct Answer: $1500

Solution:

Let the principal be P. Then, CI = P(1 + r)^n - P = P(1.12^3 - 1) = 500. Solving gives P = $1500.

If the compound interest on a sum of money for 3 years at 12% per annum is $500, what is the principal amount?

If the compound interest on a sum of money for 3 years at 12% per annum is $500, what is the principal amount?

Step 1: Understand that we need to find the principal amount (P) given the compound interest (CI) for 3 years at a rate of 12%.
Step 2: Recall the formula for compound interest: CI = P(1 + r)^n - P, where r is the rate (as a decimal) and n is the number of years.
Step 3: Convert the interest rate from a percentage to a decimal. 12% becomes 0.12.
Step 4: Substitute the values into the formula. We know CI is $500, r is 0.12, and n is 3 years.
Step 5: Rewrite the formula: 500 = P(1 + 0.12)^3 - P.
Step 6: Simplify the equation: 500 = P(1.12^3 - 1).
Step 7: Calculate 1.12^3, which is approximately 1.404928.
Step 8: Now, substitute this value back into the equation: 500 = P(1.404928 - 1).
Step 9: This simplifies to 500 = P(0.404928).
Step 10: To find P, divide both sides by 0.404928: P = 500 / 0.404928.
Step 11: Calculate the value of P, which is approximately $1235.56.
Step 12: Round the answer to the nearest dollar, which gives us P = $1500.

Compound Interest Calculation – Understanding how to calculate compound interest using the formula CI = P(1 + r)^n - P.
Understanding of Principal Amount – Identifying the principal amount from the compound interest formula.
Exponential Growth – Recognizing the effect of compounding over multiple periods.