The compound interest on a certain sum for 3 years at 8% per annum is Rs. 1,94,784. What is the simple interest on the $\frac{9}{10}$ part of the sum for the same time but at a rate of interest per annum which is $1\frac{1}{2}$ time the rate of interest per annum as applicable for compound interest?
Determine Principal Sum (P) using Compound Interest
Given: Compound Interest (CI) = Rs. 1,94,784, Rate (R) = 8% per annum = 0.08, Time (T) = 3 years. The formula for Compound Interest is: $CI = P \left( (1 + R)^T - 1 \right)$
Substituting the values: $194784 = P \left( (1 + 0.08)^3 - 1 \right)$ $194784 = P \left( (1.08)^3 - 1 \right)$ $194784 = P (1.259712 - 1)$ $194784 = P (0.259712)$
Solving for P: $P = \frac{194784}{0.259712}$ $P = 750000$ The principal sum is Rs. 7,50,000.
Calculate New Principal and Rate for Simple Interest
New Principal ($P'$): $P' = \frac{9}{10} \times P = \frac{9}{10} \times 750000 = 675000$ New Rate ($R'$): $R' = 1\frac{1}{2} \times R = 1.5 \times 8\% = 12\% = 0.12$ Time (T) remains 3 years.
Calculate Simple Interest (SI)
The formula for Simple Interest is: $SI = P' \times R' \times T$ (using R' as a decimal)
Substituting the values: $SI = 675000 \times 0.12 \times 3$ $SI = 675000 \times 0.36$ $SI = 243000$ The calculated simple interest is Rs. 2,43,000.
The correct answer provided is Option C: Rs. 2,52,000.
Important Questions from Simple and Compound Both
- The difference between the interest earned on the same amount invested under compound interest and simple interest at same rate of interest for 2 years is Rs.470. If the rate of interest is 10% p.a. then find the amount invested? (In Rs.)
- Suresh lent a sum of money on compound interest in such a way that it amounted to three times in 4 years. For how much time should he invest his money so that he gets back an amount which is 9 times of the sum of money lent by him?
- There is 60% increase in an amount in 4 years at simple interest. What will be the compound interest on Rs.49500 after 2 years at the same rate of interest? (In Rs.)
- The difference between the interest earned on the same amount invested under compound interest and simple interest at same rate of interest for 2 years is Rs.205. If the rate of interest is 5% p.a. then find the amount invested? (In Rs.)
- The difference between the interest earned on the same amount invested under compound interest and simple interest at same rate of interest for 2 years is Rs.945. If the rate of interest is 15% p.a. then find the amount invested? (In Rs.)
