Compound Discount

### Which of the following best describes a compound discount? - [x] The difference between the future value of an amount and its present discounted value. - [ ] A discount applied simply on an initial principle. - [ ] A linear reduction in the value of money over time. - [ ] The future value processed without considering present worth. > **Explanation:** Compound discount is indeed the difference between the future value of an amount and its present discounted value, considering the compounding effect of interest rates over time. ### If £200 is to be received in 5 years and is worth £170 now, what is the compound discount? - [ ] £370 - [ ] £180 - [x] £30 - [ ] £170 > **Explanation:** The compound discount would be £200 (future value) minus £170 (present value), resulting in £30. ### What does the compound discount depend on primarily? - [ ] The amount borrowed - [ ] Inflation rate - [x] The discount rate and the time period - [ ] Government policy > **Explanation:** The compound discount depends primarily on the discount rate applied and the time period over which the value is discounted. ### For investing, why is compound discount analysis important? - [ ] It increases the actual amount of money received. - [ ] It simplifies tax calculations. - [x] It helps in making informed investment decisions by realizing present value. - [ ] It decreases financial complexity. > **Explanation:** Compound discount analysis helps investors evaluate the present value of future cash flows, ensuring informed investment decisions are made. ### A higher discount rate will result in what effect on the compound discount? - [x] A higher compound discount - [ ] A lower compound discount - [ ] No effect on the compound discount - [ ] It equals present value > **Explanation:** A higher discount rate will increase the difference between the future value and the present value, leading to a higher compound discount. ### If $1,000 in 10 years is valued at $650 today, what is the compound discount? - [ ] $350 - [ ] $1,650 - [x] $350 - [ ] $650 > **Explanation:** The compound discount is $1,000 (future value) minus $650 (present value), resulting in $350. ### How would one calculate the present value given the future value and the discount rate? - [ ] PV = FV + (1 + r)^n - [x] PV = FV / (1 + r)^n - [ ] PV = FV * (1 + r)^n - [ ] PV = FV / (1 - r)^n > **Explanation:** The present value (PV) is calculated using the formula PV = FV / (1 + r)^n, where FV is future value, r is the discount rate, and n is the number of periods. ### Which of the following statements is true about compound discount? - [ ] It decreases with an increase in time period. - [ ] It increases as the inflation rate rises. - [x] It reflects the reduction of future value to present worth. - [ ] It is irrelevant in long-term investments. > **Explanation:** Compound discount reflects the reduction of future value to its present worth, highlighting the importance of the time value of money. ### What does a higher compound discount signify in a financial context? - [ ] Greater future returns - [ ] No difference in financial value - [x] More significant reduction in value over time - [ ] Steady value over time > **Explanation:** A higher compound discount signifies a more significant reduction in the value of money over time due to the discount rate and compounding period. ### Why should businesses consider compound discount in financial planning? - [x] To accurately evaluate the present value of future cash inflows/outflows - [ ] To eliminate investment risks - [ ] To track daily expenses - [ ] To simplify tax returns > **Explanation:** Businesses should consider compound discount to accurately evaluate the present value of future cash inflows/outflows, which aids prudent financial planning and investment decisions.