Properties of an ordinary annuity in engineering economy: which characteristics correctly describe such an annuity used in financial calculations?
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AIt is a series of payments (cash flows) over multiple periods.
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BAll payments are of equal amount.
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CPayments occur at equal time intervals.
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DPayments are made at the end of each period (ordinary annuity).
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EAll of these
Answer
Correct Answer: All of these
Explanation
Introduction / Context:Annuities are ubiquitous in loan amortization, lease rentals, sinking funds, and capital recovery calculations. The most common type in engineering economy is the ordinary annuity, in which equal payments occur at the end of each period. Understanding these defining features ensures correct use of P/A, A/P, F/A, and A/F factors.
Given Data / Assumptions:
- Discrete periods (monthly, quarterly, yearly, etc.).
- Constant payment amount each period.
- Timing convention: end-of-period unless stated otherwise (annuity due would be at the beginning).
Concept / Approach:With an ordinary annuity, compounding between payments is straightforward and standard factor tables apply. If payments occur at the beginning of each period, use the “annuity due” adjustment (multiply by (1 + i) where appropriate). Clarity about timing avoids misvaluation of present worth or future worth.
Step-by-Step Solution:
Identify whether cash flows are equal and periodic.Confirm end-of-period timing to classify as an ordinary annuity.Select corresponding factor (e.g., F/A, i, n for accumulation; P/A, i, n for present worth).Verification / Alternative check:
Cross-check by constructing a small amortization schedule and confirming that interest accrues between payments.Why Other Options Are Wrong:
Options a–d together define an ordinary annuity; each alone is incomplete, hence “All of these.”Common Pitfalls:
Accidentally valuing an annuity due with ordinary annuity factors, leading to underestimation by a factor of (1 + i).Mixing equal-payment annuities with gradients or geometric growth without using the proper combined factors.Final Answer:
All of these