--- title: "Define equivalent worth and ROR; deposit to draw monthly" subject: "Engineering Economics" chapter: 2 key: "semester_6/engineering_economics:equivalent-worth-ror-draw-monthly-10000" source: https://www.bctengineer.com/q/semester_6/engineering_economics/equivalent-worth-ror-draw-monthly-10000 site: BCT Engineering --- # Define equivalent worth and ROR; deposit to draw monthly Engineering Economics · Chapter 2: Interest and Time Value of Money - Asked in: 2070 Magh, 2+4 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/engineering_economics/equivalent-worth-ror-draw-monthly-10000 - Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-2 ## Question Define equivalent worth and rate of return method. How much rupees should you deposit now in a bank account that gives 8% interest per year if you wish to draw Rs. 10,000 per month for 10 years? ## Short answer Equivalent worth is the value at a single date of cash flows moved at the MARR. Rate of return is the interest rate that makes PW of net cash flow zero, accepted if ≥ MARR. Deposit needed: Rs 824,215 (8% per year compounded monthly, 120 withdrawals of Rs 10,000). ## Answer #### Equivalent worth Equivalent worth is the value, at one chosen date, of a whole set of cash flows when each flow is moved to that date using the interest rate (MARR). Cash flows at different times become comparable only after this move. Three forms are used: present worth (PW) at time 0, future worth (FW) at the end of the project, and annual worth (AW) as a uniform yearly amount. #### Rate of return (ROR) method The ROR (internal rate of return) is the interest rate *i\** at which the PW (or AW, FW) of the net cash flow is zero, i.e. PW of inflows = PW of outflows. The project is accepted if *i\** ≥ MARR. It is found by trial and error with interpolation. #### Numerical: deposit needed Assumption: 8% per year is the nominal rate, compounded monthly. Withdrawals are at the end of each month, so this is an annuity. ```text P = ? | 0 1 2 3 ... 119 120 (months) ↑ ↑ ↑ ↑ ↑ 10,000 each month (A) ``` - Monthly interest i = 8% / 12 = 0.6667% = 0.006667 - Number of months n = 10 × 12 = 120 - P = A (P/A, i, n) - (P/A, 0.6667%, 120) = [1 − (1.006667)^-120] / 0.006667 = 82.4215 - P = 10,000 × 82.4215 = Rs 824,214.81 **Answer: Rs 824,215 should be deposited now (about Rs 8.24 lakh).** If 8% is taken as the effective annual rate, monthly i = (1.08)^(1/12) − 1 = 0.6434% and P = Rs 834,324. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is equivalent worth? A. Sum of cash flows without interest B. Value at one chosen date of a set of cash flows moved to that date at the interest rate C. Average cash flow D. Salvage value Answer: B. Moving flows to one date makes them comparable. (Key point: Equivalent worth) 2. How is the rate of return defined? A. The MARR itself B. The rate with maximum PW C. The rate i* at which PW (or AW, FW) of the net cash flow is zero; accept if i* >= MARR D. Interest on the loan Answer: C. IRR makes PW of inflows equal PW of outflows. (Key point: ROR) 3. Deposit for Rs 10,000/month for 10 years at 8% nominal monthly? A. 10,000 x 120 B. 10,000 (F/A, 0.6667%, 120) C. 10,000 (P/A, 8%, 10) D. P = 10,000 (P/A, 0.6667%, 120) = about Rs 824,215 Answer: D. Monthly rate 0.6667%, n = 120. 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