Important GRE Words
November 29, 2017
Journey of Headlamps
December 12, 2017

Time value of money

Interest is the cost of using capital. If you trace back to the pages of history, you can find the signs of Interest in the recorded transactions. Before the term money was coined, capital was represented by wealth in the form of personal possessions, and interest was paid in kind. In the modern world we have developed different kinds of credit instruments and banking system. Business and Banks are the biggest borrowers. Business seek the the use of capital goods to increase the productivity. Governments borrow against future tax revenues to finance highways, welfare and public services.

Nearly everyone is directly or indirectly exposed to interest transactions occasionally or regularly. Lets understand the reasons for Interest, how they are calculated and realize their effect on cash flows. Interest is the premium paid to compensate a lender for the administrative cost of making a loan, the risk of non-repayment, and the loss of the use of the loaned amount(opportunity cost). So Interest represents the earning power of money. A borrower pays interest charges for the opportunity to do something now that otherwise would have to be delayed or would never be done.

                                                                TVM Formula

Simple Interest I is a charge directly proportional to the capital loaned at rate i for N periods, So that I = PiN. Compound interest includes charges for the accumulated interest as well as the amount of unpaid principal. Time value mechanics involve the use of compound-interest factors to translate payments of various amounts occurring at various times to a single equivalent payment. So an EMI (Easy Monthly Installments) or Annuity Payment is a series of equal payments, at equal intervals, with the first payment at the end of first period.

Basic Time Value of Money Formula

Depending on the exact situation in question, the TVM (Time value of Money) formula may change slightly. For example, in the case of annuity or perpetuity payments, the generalized formula has additional or less factors. But in general, the most fundamental TVM formula takes into account the following variables:

  • FV = Future value of money
  • PV = Present value of money
  • i = interest rate
  • n = number of compounding periods per year
  • t = number of years

Based on these variables, the formula for TVM is:

FV = PV x [ 1 + (i / n) ] (n x t)

TVM Example

Assume a sum of $10,000 is invested for one year at 10% interest. The future value of that money is:

FV = $10,000 x (1 + (10% / 1) ^ (1 x 1) = $11,000

The formula can also be rearranged to find the value of the future sum in present day dollars. For example, the value of $5,000 one year from today, compounded at 7% interest, is:

PV = $5,000 / (1 + (7% / 1) ^ (1 x 1) = $4,673

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