Difficulty: Easy
Correct Answer: Capital recovery annuity
Explanation:
Introduction / Context:Debt service for capital projects is often structured so that a constant payment each period covers both interest and a portion of principal, fully recovering the initial investment over time. In engineering economy, this pattern is captured by the capital recovery annuity and corresponding factor A/P (capital-recovery factor).
Given Data / Assumptions:
Concept / Approach:The capital recovery factor converts a present amount P into a uniform series A: A = P * (A/P, i, n). Each payment A consists of interest on the outstanding balance plus principal reduction. By the final period, the principal is fully repaid. This structure underlies loan amortization and lease-equivalent calculations.
Step-by-Step Solution:
Express A = P * [i(1 + i)^n / ((1 + i)^n − 1)].Construct an amortization schedule to show interest and principal components each period.Verify that the remaining balance declines to zero after n payments.Verification / Alternative check:
Check that present worth of all A payments discounted at i equals P, confirming full capital recovery.Why Other Options Are Wrong:
Present worth annuity: refers to discounting an annuity to time zero, not debt service recovery per se.Sinking fund annuity: accumulates to a future sum, typically separate from debt payments.Compound annuity/deferred annuity: different timing/structure; not the standard debt service construct.Common Pitfalls:
Confusing sinking funds (future buildup) with capital recovery (level payments that retire P and interest).Ignoring fees or balloon payments that alter equal-payment assumptions.Final Answer:
Capital recovery annuity
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