Difficulty: Easy
Correct Answer: Both (a) and (b)
Explanation:
Introduction / Context:Engineering-economy factor notation compresses key parameters into a readable tag. The Capital Recovery Factor (CRF), often written A/P, converts a present amount P into an equal annual amount A over n periods at interest rate i. Interpreting the compact label correctly avoids factor-table and calculator input errors.
Given Data / Assumptions:
Concept / Approach:The functional form is A = P * [i(1 + i)^n / ((1 + i)^n − 1)]. When you see CRF − 8% − 7, substitute i = 0.08 and n = 7. The same convention applies to other factors (P/A, F/A, P/F, etc.), where the trailing numbers specify interest and period count.
Step-by-Step Solution:
Map the notation: CRF(EP) − 8% − 7 → i = 8% per year, n = 7 years.Compute A/P for those inputs if needed to obtain the annual recovery A from present P.Use A to build amortization or capital-charge schedules.Verification / Alternative check:
Confirm by deriving A/P via a financial calculator or spreadsheet: A = PMT(rate=0.08, nper=7, pv=−P).Why Other Options Are Wrong:
“Neither (a) nor (b)” rejects the standard convention; “Only (a)” ignores the periods parameter, which is essential to the factor.Common Pitfalls:
Confusing “per year” with per period when periods are not annual; always align i with the compounding period.Misreading the factor as P/A instead of A/P, leading to inverted results.Final Answer:
Both (a) and (b)
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