--- title: "Find X from cash flow diagram, 1% per month" subject: "Engineering Economics" chapter: 2 key: "semester_6/engineering_economics:find-x-cash-flow-monthly-interest" source: https://www.bctengineer.com/q/semester_6/engineering_economics/find-x-cash-flow-monthly-interest site: BCT Engineering --- # Find X from cash flow diagram, 1% per month Engineering Economics · Chapter 2: Interest and Time Value of Money - Asked in: 2076 Shrawan, 3 marks - Video: [Economic Equivalence - How to Equate Two Cash Flow Diagrams - Engineering Economics](https://www.youtube.com/watch?v=62wSuWUWI_0) — AF Math & Engineering - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/engineering_economics/find-x-cash-flow-monthly-interest - Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-2 ## Question Find the value of X from the following figure. i = 1% per month. [Figure: Rs 15000 outflow at time 0; X received at 2, X received at 6, and 2X received at 10 years, as marked on the diagram] ## Short answer Convert 1% per month to effective annual rate 12.6825%. Equate present worth of outflows and inflows: 15,000 = X(P/F,12.68%,2) + X(P/F,12.68%,6) + 2X(P/F,12.68%,10). Result: X = Rs 7,970. ## Answer #### Assumptions The figure shows the times (2, 6, 10) in years, while the rate is 1% per month, so the equivalent yearly rate is needed: i = (1.01)^12 − 1 = **12.6825% per year**. (If the times are actually months, use 1% directly; see the end.) #### Cash flow diagram (text) ```text X X 2X ^ ^ ^ -------+----------+----------------+--> time 0 2 6 10 | v 15,000 ``` #### Equation (present worth at time 0) Outflow = Inflows: 15,000 = X (P/F, i, 2) + X (P/F, i, 6) + 2X (P/F, i, 10) With i = 12.6825%: - (P/F, i, 2) = 1/(1.126825)² = 0.78757 - (P/F, i, 6) = 1/(1.126825)⁶ = 0.48850 - (P/F, i, 10) = 1/(1.126825)¹⁰ = 0.30299 15,000 = X (0.78757 + 0.48850 + 2 × 0.30299) = X (1.88206) X = 15,000 / 1.88206 = **Rs 7,970** **Answer: X = about Rs 7,970.** If the points 2, 6, 10 are months at 1% per month, the factors are 0.98030, 0.94205 and 0.90529, so X = 15,000 / (0.98030 + 0.94205 + 2 × 0.90529) = 15,000 / 3.7329 = Rs 4,018. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Times are in years but rate is 1% per month. What is the yearly rate? A. 12% B. 1% C. (1.01)^2 - 1 D. (1.01)^12 - 1 = 12.6825% Answer: D. The monthly rate is converted to an effective annual rate. (Key point: Rate conversion) 2. Which equation is solved? A. 15,000 = X(P/F,i,2) + X(P/F,i,6) + 2X(P/F,i,10) B. 15,000 = X + X + 2X C. 15,000 = X(F/P,i,2) + X(F/P,i,6) + 2X(F/P,i,10) D. 15,000 = 4X(P/A,i,10) Answer: A. Equating present worths of the inflows to the outflow. (Key point: Equation) 3. What is X when the times are years? A. About Rs 4,018 B. About Rs 7,970 C. About Rs 3,750 D. About Rs 15,000 Answer: B. X = 15,000/1.88206 = 7,970; Rs 4,018 applies only if the times were months. 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