Asked by Jayla Barwari on Jun 30, 2024
Verified
What single rate of discount would be equivalent to a series of 25%/18%/10%?
A) 55.4%
B) 53.0%
C) 41.7%
D) 34.3%
E) 44.7%
Discount Rate
In finance, it is the interest rate used to determine the present value of future cash flows, or the rate at which a bank lends to other banks or financial institutions.
Series Discount
A set of multiple discounts applied one after the other on a product’s price.
- Determine the cumulative single discount rate derived from several individual discounts.
Verified Answer
ZK
Zybrea KnightJul 05, 2024
Final Answer :
E
Explanation :
To find the single equivalent discount rate for a series of discounts, we use the formula for successive discounts: Net Price Factor=(1−d1)(1−d2)(1−d3) \text{Net Price Factor} = (1 - d_1)(1 - d_2)(1 - d_3) Net Price Factor=(1−d1)(1−d2)(1−d3) , where d1,d2,d_1, d_2, d1,d2, and d3d_3d3 are the decimal forms of the discounts. For 25%, 18%, and 10%, we have d1=0.25d_1 = 0.25d1=0.25 , d2=0.18d_2 = 0.18d2=0.18 , and d3=0.10d_3 = 0.10d3=0.10 . Thus, the Net Price Factor = (1−0.25)(1−0.18)(1−0.10)=0.75×0.82×0.90(1 - 0.25)(1 - 0.18)(1 - 0.10) = 0.75 \times 0.82 \times 0.90(1−0.25)(1−0.18)(1−0.10)=0.75×0.82×0.90 . Calculating this gives a Net Price Factor of approximately 0.553. The equivalent single discount is 1−Net Price Factor=1−0.553=0.4471 - \text{Net Price Factor} = 1 - 0.553 = 0.4471−Net Price Factor=1−0.553=0.447 or 44.7%.
Learning Objectives
- Determine the cumulative single discount rate derived from several individual discounts.
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