Article:Time value of money application and rationality an approach using differential equations and definite integrals.
ArticleTITLETime value of money application and rationality an approach usingdifferential equations and definite integrals.BYPARVEZ, MAHBUBDAFFODIL INTERNATIONAL UNIVERSITYCONCEPTThis article is about the importance of time value of money. As the time value of money is one ofthe important factor in making the financial decision because it include the concept of interest,amortization, present value, annuities, creation of sinking fund, etc. The problems concerningthe time value of money which involves the calculation of compound interest and future valueare often solve by algebraic formulae. This article also solve these problem using differentialequation and integral techniques. It also compare the both method algebraic formulae anddifferential and integral techniques.EXPLANATIONTime value of money is the key factor of financial decision and finance. Value of moneydecrease with the passage of time so we need to adjust value of money with time. This conceptof synchronizing the money with time is called time value of money.In this article the researcher solve the time value of money by using differential equation anddefinite integral.
By comparing the algebraic formulae and the definite integral and differential technique we getthe following results.1) Compound interest and FVBy measuring the compound interest and FV with both methods we found 45% errorwhich is not significant.2) Ordinary annuity: FVBy measuring the FV of annuity with both methods we found 40% error which is notsignificant.3) Ordinary annuity: sinking fundBy measuring the FV of annuity of sinking fund (a fund into which periodic payments aremade in order to accumulate a specific) with both methods we found 40% error which isnot significant.4) Ordinary Annuity: present value5) By measuring the PV of ordinary annuity with both methods we found 20% error which isnegligible amount.6) Ordinary annuity: amortization7) By measuring the loan amortization (dividing loan payments into equal payments) withboth methods we found 21% which is very insignificant.CONCLUSIONThis article gently explained the importance of time value of money. The researchersmeasure the future value and compounded interest payment by using both methodalgebraic and definite integral and differential equation. It also compare both methodand analyze the error.By using the above techniques we found that there is little error and all the level oferrors are not significant. We conclude that there is little amount of error by usingboth methods. So measuring time value of money by using both method give correctresults.