Time value of money fundamentals: which statements correctly describe interest, principal, and the concept itself in engineering economy?
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AThe change in the amount of money over time is termed the “time value” of money.
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BThe manifestation of the time value of money is called interest.
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CInterest on borrowing equals the present amount owed minus the original loan.
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DThe original investment or loan amount is called the principal.
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EAll of these.
Answer
Correct Answer: All of these.
Explanation
Introduction / Context:The time value of money (TVM) recognizes that a rupee today is worth more than a rupee tomorrow because of earning potential, risk, and preference. TVM underpins every valuation in engineering economy, from project appraisal to loan structuring and asset replacement analysis.
Given Data / Assumptions:
- Discrete compounding periods.
- Positive interest rates unless stated otherwise.
- Clear distinction between principal and interest.
Concept / Approach:Interest quantifies how money grows (or costs) over time. On a loan, interest accrued equals the amount owed at a given time minus the initial principal, net of any interim repayments. Principal is the base amount on which interest is computed. Together, these define the mechanics of discounting (present worth) and compounding (future worth).
Step-by-Step Solution:
State TVM: value changes with time due to opportunity cost and risk.Define interest as the numerical expression of that change (growth or cost).Define principal as the original base amount; interest on borrowing = current outstanding − original loan, adjusted for any repayments.Verification / Alternative check:
Validate with a simple compounding example: P grows to F = P(1 + i)^n; interest accrued over n periods = F − P.Why Other Options Are Wrong:
Options a–d are all correct and complementary; only “All of these” captures the full concept.Common Pitfalls:
Confusing nominal and effective rates; always align the compounding frequency with cash-flow timing.Ignoring inflation when interpreting real versus nominal returns.Final Answer:
All of these.