The difference between compound and simple interest on Rs. 15,000 over 2 years is Rs. 96. What is the annual interest rate?
Show answer Hide answer
Answer: A. 8
Explanation
The difference between compound and simple interest over a two-year period is given by the formula principal times the square of the rate percentage. Substituting the given difference of ninety-six and the principal of fifteen thousand into the formula gives ninety-six equals fifteen thousand times r over one hundred squared. Solving this equation for r yields an annual interest rate of eight percent. The two-year interest difference formula isolates the exact impact of compounding interest on a given principal sum. Algebraic rearrangement allows the unknown interest rate to be extracted from the difference equation. Percentage rates in interest formulas are expressed as decimals by dividing the rate value by one hundred.
Option B yields an interest difference of one hundred fifty when tested against the fifteen thousand principal. Option C produces an interest difference of two hundred sixteen, which is much higher than ninety-six. Option D is incorrect because the rate can be definitively determined using the provided algebraic formula.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. Sunil earned Rs.2828.80 in compound interest over two years at 8% p.a. What total sum (principal plus interest) did he receive at the end?
Show answer Hide answer
Answer: B. Rs.19,828.80
Calculating the compound interest over two years at eight percentage per annum gives the exact interest earned. Adding this earned compound interest to the unknown initial principal determines the total accumulated sum r...
Q2. The difference between compound and simple interest on Rs. 15,000 for 2 years is Rs. 96. What is the annual interest rate?
Show answer Hide answer
Answer: A. 8
The difference between compound and simple interest over two years follows a specific algebraic formula. Substituting the given difference and principal into the formula isolates the squared interest rate. Solving for th...
Q3. The difference between compound and simple interest on Rs. 5000 for 2 years is Rs. 72. Find the annual interest rate:___________?
Show answer Hide answer
Answer: D. 12%
The two-year difference between compound and simple interest equals principal times rate squared. Dividing the 72 rupee difference by the 5000 rupee principal gives zero point zero 144. Taking the square root and multipl...
Q4. A canal's trapezoidal cross-section has a 10 m top width, 6 m bottom width, and a 640 sq m area. Find the canal depth_________?
Show answer Hide answer
Answer: D. 80 m
The area of a trapezoidal cross-section equals one-half times the sum of the parallel top and bottom widths times depth. Substituting the given values gives six hundred forty equals one-half times ten plus six times dept...
Q5. A square has a 4√2 cm diagonal. What is the diagonal of another square whose area is double the first__________?
Show answer Hide answer
Answer: A. 8cm
The side length of the original square is derived from its given diagonal measurement. Doubling the area of the first square gives a new area value of thirty two square units. Calculating the diagonal of the new square y...
Q6. The difference between a number and its two-fifths is 510. What is 10% of that number?
Show answer Hide answer
Answer: B. 85
Subtracting two-fifths from a whole number leaves three-fifths of the original number. Setting three-fifths of the number equal to 510 yields an original number of 850. Calculating ten percent of 850 results in the final...