If the true discount on a sum of money is $200 and the rate of interest is 10% p

If the true discount on a sum of money is $200 and the rate of interest is 10% per annum for 2 years, what is the present worth?

If the true discount on a sum of money is $200 and the rate of interest is 10% per annum for 2 years, what is the present worth?

Step 1: Understand that True Discount is the difference between the Present Worth and the Future Value.
Step 2: Identify the given values: True Discount = $200, Rate of Interest = 10% per annum, Time = 2 years.
Step 3: Use the formula for True Discount: True Discount = Present Worth * Rate * Time / 100.
Step 4: Let Present Worth be represented as 'x'. So, we rewrite the formula as: 200 = x * 10 * 2 / 100.
Step 5: Simplify the equation: 200 = x * 20 / 100.
Step 6: Multiply both sides by 100 to eliminate the fraction: 200 * 100 = x * 20.
Step 7: Calculate the left side: 20000 = x * 20.
Step 8: Divide both sides by 20 to solve for x: x = 20000 / 20.
Step 9: Calculate the value of x: x = 1000.
Step 10: Conclude that the Present Worth is $1000.

True Discount – True discount is the difference between the future value and the present worth, calculated based on the interest rate and time period.
Present Worth – Present worth is the current value of a sum of money that will be received in the future, discounted at a specific interest rate.
Interest Rate Calculation – Understanding how to apply the interest rate over a specified time period to calculate present worth.