Capital Recovery Factor notation: CRF(EP) − 8% − 7 is interpreted how? Identify what the “8%” and the “7” specify in this factor label.

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:

  • CRF(EP) refers to A/P (capital recovery) for end-of-period payments.
  • “8%” denotes the nominal interest rate per year for the periods considered.
  • “7” denotes the number of periods (years) n.


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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