Asked by Vanessa Garcia on Apr 24, 2024
Verified
What single rate of discount would be equivalent to a series of 15% / 8% / 4%?
A) 48.0%
B) 27.0%
C) 24.9%
D) 9.99%
E) 21.4%
Single Rate
A fixed interest rate that remains constant throughout the term of the loan or investment.
Discount
A reduction applied to the regular price of goods or services, usually offered to encourage purchase or reward customers.
Series
A sequence of numbers or terms that follow a specific pattern.
- Understand and calculate equivalent single rates of discounts from a series.
Verified Answer
JB
Joaquin Bueno7 days ago
Final Answer :
C
Explanation :
To find the single equivalent discount rate for a series of discounts, we use the formula for successive discounts: 1−(1−d1)(1−d2)(1−d3)1 - (1 - d_1)(1 - d_2)(1 - d_3)1−(1−d1)(1−d2)(1−d3) , where d1,d2,d3d_1, d_2, d_3d1,d2,d3 are the decimal forms of the discounts. For 15%, 8%, and 4%, the calculation is 1−(1−0.15)(1−0.08)(1−0.04)=1−(0.85)(0.92)(0.96)=1−0.7512=0.24881 - (1 - 0.15)(1 - 0.08)(1 - 0.04) = 1 - (0.85)(0.92)(0.96) = 1 - 0.7512 = 0.24881−(1−0.15)(1−0.08)(1−0.04)=1−(0.85)(0.92)(0.96)=1−0.7512=0.2488 , or 24.88%, which rounds to 24.9%.
Learning Objectives
- Understand and calculate equivalent single rates of discounts from a series.
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