Question

In how many years will Rs.15,000 become Rs.19,500 at 5% simple interest per annum?

• A. 4 years
• B. 8 years
• C. 5 years
• D. 6 years

Hint:

First find simple interest by subtracting principal from amount, then apply the SI formula.

Answer 1

The Correct Option is D

To find out in how many years Rs. 15,000 will become Rs. 19,500 at a simple interest rate of 5% per annum, we will use the formula for simple interest:

\(S.I. = \frac{P \times R \times T}{100}\)

• \(S.I.\) is the simple interest.
• \(P = 15000\) is the principal amount.
• \(R = 5\%\) is the rate of interest per annum.
• \(T\) is the time in years.

Given that the amount becomes Rs. 19,500, we first calculate the total interest earned:

Total amount = Principal amount + Simple Interest

\(19500 = 15000 + \text{S.I.}\)

Therefore, \(\text{S.I.} = 19500 - 15000 = 4500\)

Substitute the known values into the formula for simple interest:

\(4500 = \frac{15000 \times 5 \times T}{100}\)

Simplifying gives:

\(4500 = \frac{75000 \times T}{100}\)

Eliminate the fraction by multiplying both sides by 100:

\(450000 = 75000 \times T\)

Now solve for \(T\):

\(T = \frac{450000}{75000}\)

\(T = 6\)

Therefore, the time required for Rs. 15,000 to become Rs. 19,500 at 5% simple interest per annum is 6 years.

Calculation Step	Reason
Calculate Simple Interest (S.I.)	S.I. = Total Amount - Principal = 19,500 - 15,000 = 4,500
Use the S.I. formula	S.I. = (P × R × T) / 100 = 4,500
Solve for T	4,500 = (15,000 × 5 × T) / 100; T = 6 years