A sum of money becomes $1200 in 3 years at simple interest. If the rate of inter

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Question: A sum of money becomes $1200 in 3 years at simple interest. If the rate of interest is 5% per annum, what was the principal?

Options:

Correct Answer: $1000

Solution:

Let the principal be P. Then, A = P + SI = P + (P × 0.05 × 3) = 1200. Solving gives P = $1000.

A sum of money becomes $1200 in 3 years at simple interest. If the rate of interest is 5% per annum, what was the principal?

A sum of money becomes $1200 in 3 years at simple interest. If the rate of interest is 5% per annum, what was the principal?

Step 1: Understand that the total amount (A) after 3 years is $1200.
Step 2: Know that the formula for total amount with simple interest is A = P + SI, where SI is the simple interest.
Step 3: The simple interest (SI) can be calculated using the formula SI = P × r × t, where r is the rate of interest and t is the time in years.
Step 4: In this case, the rate (r) is 5% per annum, which is 0.05 in decimal form, and the time (t) is 3 years.
Step 5: Substitute the values into the simple interest formula: SI = P × 0.05 × 3.
Step 6: This simplifies to SI = 0.15P.
Step 7: Now substitute SI back into the total amount formula: A = P + SI becomes 1200 = P + 0.15P.
Step 8: Combine like terms: 1200 = 1.15P.
Step 9: To find P, divide both sides by 1.15: P = 1200 / 1.15.
Step 10: Calculate P, which gives P = $1000.

Simple Interest Calculation – Understanding how to calculate simple interest and its relation to principal, rate, and time.