Article:Time value of money application and rationality an approach using differential equations and definite integrals.
1. Article
TITLE
Time value of money application and rationality an approach using
differential equations and definite integrals.
BY
PARVEZ, MAHBUB
DAFFODIL INTERNATIONAL UNIVERSITY
CONCEPT
This article is about the importance of time value of money. As the time value of money is one of
the 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 concerning
the time value of money which involves the calculation of compound interest and future value
are often solve by algebraic formulae. This article also solve these problem using differential
equation and integral techniques. It also compare the both method algebraic formulae and
differential and integral techniques.
EXPLANATION
Time value of money is the key factor of financial decision and finance. Value of money
decrease with the passage of time so we need to adjust value of money with time. This concept
of 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 and
definite integral.
2. By comparing the algebraic formulae and the definite integral and differential technique we get
the following results.
1) Compound interest and FV
By measuring the compound interest and FV with both methods we found 45% error
which is not significant.
2) Ordinary annuity: FV
By measuring the FV of annuity with both methods we found 40% error which is not
significant.
3) Ordinary annuity: sinking fund
By measuring the FV of annuity of sinking fund (a fund into which periodic payments are
made in order to accumulate a specific) with both methods we found 40% error which is
not significant.
4) Ordinary Annuity: present value
5) By measuring the PV of ordinary annuity with both methods we found 20% error which is
negligible amount.
6) Ordinary annuity: amortization
7) By measuring the loan amortization (dividing loan payments into equal payments) with
both methods we found 21% which is very insignificant.
CONCLUSION
This article gently explained the importance of time value of money. The researchers
measure the future value and compounded interest payment by using both method
algebraic and definite integral and differential equation. It also compare both method
and analyze the error.
By using the above techniques we found that there is little error and all the level of
errors are not significant. We conclude that there is little amount of error by using
both methods. So measuring time value of money by using both method give correct
results.