Determine the single equivalent rate of discount for the discount series 24%, 13%, and 9%.(1 - d1) = (1 - d2) = (1 - d3) = 1 - [(1 - d1)(1 - d2)(1 - d3)] = (rounded to four decimal places)Single Equivalent Rate of Discount = % (rounded to two decimal places)
Question
Determine the single equivalent rate of discount for the discount series 24%, 13%, and 9%.(1 - d1) = (1 - d2) = (1 - d3) = 1 - [(1 - d1)(1 - d2)(1 - d3)] = (rounded to four decimal places)Single Equivalent Rate of Discount = % (rounded to two decimal places)
Solution
To determine the single equivalent rate of discount for the discount series 24%, 13%, and 9%, you need to use the formula:
1 - [(1 - d1)(1 - d2)(1 - d3)]
where d1, d2, and d3 are the discount rates.
Step 1: Convert the percentages to decimals. So, d1 = 0.24, d2 = 0.13, and d3 = 0.09.
Step 2: Substitute the values into the formula:
1 - [(1 - 0.24)(1 - 0.13)(1 - 0.09)]
Step 3: Calculate the expression in the brackets:
= 1 - [(0.76)(0.87)(0.91)]
Step 4: Multiply the values:
= 1 - [0.602472]
Step 5: Subtract the result from 1:
= 0.397528
Step 6: Convert the decimal back to a percentage:
= 39.75% (rounded to two decimal places)
So, the single equivalent rate of discount for the discount series 24%, 13%, and 9% is approximately 39.75%.
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