--- title: "Monthly deposits with quarterly compounding, future amount" subject: "Engineering Economics" chapter: 2 key: "semester_6/engineering_economics:deposit-quarterly-monthly-five-years" source: https://www.bctengineer.com/q/semester_6/engineering_economics/deposit-quarterly-monthly-five-years site: BCT Engineering --- # Monthly deposits with quarterly compounding, future amount Engineering Economics · Chapter 2: Interest and Time Value of Money - Asked in: 2076 Shrawan, 3 marks - Video: [Compounding More Frequent than Payments - Engineering Economics Lightboard](https://www.youtube.com/watch?v=kEcGEXlK5oY) — Engineering Economics Guy - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/engineering_economics/deposit-quarterly-monthly-five-years - Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-2 ## Question What will be the amount at the end of 10 years if you deposit Rs 5000 per month for five years continuously if nominal interest rate is 10% compounded quarterly? ## Short answer Effective monthly rate = (1.025)^(1/3) - 1 = 0.8265%. First find FV after 5 years of monthly Rs 5,000: Rs 3,86,345. Then compound that amount 5 more years at 2.5% quarterly: F10 = 3,86,345 × (1.025)^20 = Rs 6,33,072. ## Answer #### Approach Deposits are monthly but interest is compounded quarterly, so find the equivalent **interest rate per month**, then compound the five-year amount for the next five years. Nominal rate 10% compounded quarterly: i per quarter = 10%/4 = 2.5% Effective monthly rate: i_m = (1.025)^(1/3) − 1 = **0.8265% per month** ```text Deposits 5000 each month, months 1..60 (5 years) |-----------------------|-----------------------| 0 60 120 months deposits -> F5 = ? F10 = ? ``` #### Step 1: Amount at end of year 5 F5 = 5,000 (F/A, 0.8265%, 60) (1.008265)^60 = (1.025)^20 = 1.63862 (F/A, 0.8265%, 60) = (1.63862 − 1) / 0.008265 = 77.269 F5 = 5,000 × 77.269 = Rs 386,345 #### Step 2: Grow for the next 5 years (no deposits) F10 = F5 (F/P, 2.5%, 20) = 386,345 × 1.63862 = **Rs 633,072** **Answer: Amount at the end of 10 years = about Rs 6.33 lakh (Rs 633,000).** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why is an equivalent monthly rate needed? A. Deposits are monthly but interest is compounded quarterly B. Because the rate is nominal 10% per year C. Because deposits stop after 5 years D. Because the rate changes monthly Answer: A. Payment period and compounding period differ, so the rate is converted to the payment period. (Key point: Why convert monthly rate) 2. What is the effective monthly rate? A. 10%/12 = 0.8333% B. (1.025)^(1/3) - 1 = 0.8265% C. 2.5%/3 = 0.8333% D. 10%/4 = 2.5% Answer: B. A quarter's 2.5% is split compoundingly into three months. (Key point: Monthly rate) 3. What is done after year 5 when deposits stop? A. Continue the annuity for 5 more years B. Divide F5 by 20 C. Compound F5 for 5 more years: F10 = F5 (F/P, 2.5%, 20) D. Add 5,000 x 60 to F5 Answer: C. No further deposits, so only the lump sum is compounded. (Key point: Years 5-10) ## Related in Engineering Economics - [Monthly deposits, quarterly compounding, balance at year 8](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Aequal-monthly-deposits-balance-8-years) — Engineering Economics, chapter 2 - [Compounding semi-annually and monthly, 10% nominal](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Adeposit-10000-semiannual-monthly) — Engineering Economics, chapter 2 - [Deposit now to draw growing monthly amount](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Adeposit-now-growing-withdrawal) — Engineering Economics, chapter 2 - [Nominal vs effective rate; quarterly rate from monthly](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Anominal-effective-monthly-1-quarterly) — Engineering Economics, chapter 2 - [Nominal vs effective; FW with monthly compounding](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Afw-monthly-compounding-annual-begin) — Engineering Economics, chapter 2, asked 2× - [Simple vs compound interest; number of deposits](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Asimple-vs-compound-deposits-20-lakh) — Engineering Economics, chapter 2 ## Related in other subjects - [Best installed capacity at 10% interest](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Abest-installed-capacity-10pct) — Hydro Power, chapter 3