A sum of money is invested at 10% per annum for 4 years. If the true discount is

₹0.0

Question: A sum of money is invested at 10% per annum for 4 years. If the true discount is $400, what is the sum?

Options:

Correct Answer: $4400

Solution:

Let the sum be x. True Discount = x * Rate * Time / 100. 400 = x * 10 * 4 / 100. Solving gives x = $4000.

A sum of money is invested at 10% per annum for 4 years. If the true discount is $400, what is the sum?

A sum of money is invested at 10% per annum for 4 years. If the true discount is $400, what is the sum?

Step 1: Understand that we need to find the sum of money, which we will call 'x'.
Step 2: Know that the true discount formula is: True Discount = (Sum * Rate * Time) / 100.
Step 3: Substitute the known values into the formula: True Discount = 400, Rate = 10%, Time = 4 years.
Step 4: Write the equation: 400 = (x * 10 * 4) / 100.
Step 5: Simplify the equation: 400 = (40x) / 100.
Step 6: Multiply both sides by 100 to eliminate the fraction: 40000 = 40x.
Step 7: Divide both sides by 40 to solve for x: x = 40000 / 40.
Step 8: Calculate the result: x = 1000.
Step 9: Realize that the true discount of $400 corresponds to a sum of $4000 when considering the interest over 4 years.

True Discount – True discount is the difference between the present value and the future value of a sum of money, calculated based on the interest rate and time period.
Simple Interest – The calculation of interest on a principal sum over a specified period at a fixed rate.
Basic Algebra – The use of algebraic manipulation to solve for an unknown variable in an equation.