Mathematics of Finance

Mathematics of Finance

If a firm borrows fund from a financial institution, it receives cash flow and commits an obligation to pay cash for interest and repay principal in the future period.

Time value of money is an individual preference for possession of a given amount of money now rather than the same amount of money at future time..

Simple interest: This is an interest cost for one or more period where a principal amount of money, on which interest is computed, remains the same from time to time.

It is calculated using the formula;  I = PRT where p = principal amount, R = interest rate in decimal (e.g 20% is 0.20) and T= time 

 Example:

John borrowed $20000 for a period of 5 years at an interest rate of 8%. How much would he pay back at the end of the period?

            SOLUTION 

I=PRT        p=$20000, R= 8% =0.08, t=5

 I= 20000 x 0.08 x 5

   =$8000 

At the end of 5 years, he would pay principal amount + interest, $20000 +$8000=$28000.

  Compound interest 

This is the interest cost for two or more periods when after each period, interest earned in that period is added to amount on which interest is computed for future period. Simply,the financial sum is increased at the end of each period by interest earned in that period.

 Compounding is the process of calculating future value of cash flow

Discounting is the process of calculating present value of cash flow.

 Future value is the amount an investment will be worth at a future date if invested at compound interest. It is the sum of principal amount and interest. It is calculated using the formula;                      F=P(1+r)ⁿ

Example: if you invest $200 in a bank account at 10% interest rate for two years. How much future sum would you receive after one year?

                            SOLUTION 

 p=$200   r = 10% =0.10

   F=P(1+r)ⁿ

  F=200(1+0.10)² 

  =200(1.10)²

      ^{=200 x 1.21}

     ^=$242

 ^{You would receive $242 after two years if invested at compound interest.}

                

                      ^{Future Value of an Annuity}  

     ^{Annuity is a fixed amount paid or received each year for a specified number of years. It is calculated using the formula;} 

         FVA = C  [(1+r)ⁿ-1]

                                 r             

  ^{where c= cash flow, n= number of period, r= rate of interest, FVA= future value of annuity.}

                                        ^{Sinking Fund} 

  ^{It is a fund which is created out of fixed payment each period to accumulate a future sum after a specified period.}

 It is calculated using the formula;       

s.f=  f.v [     r       ]

                  [(1+r)ⁿ-1]

                                                                               

Example: 15 semiannual payments made into sinking fund at 7% are compounded so that $4850 will be present. Calculate the amount of each payment. Give your answer in the nearest cent.
Solution