Mathematical Theory of Interest
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Interest is basically the price of asset that is borrowed. It is paid in the case of borrowed money, in the purchase of shares and goods through hire purchase. There are different types of interest and each may be calculated using a mathematical formula.
The mathematical approaches to the theory of interest is given under the following heads:Simple Interest
Calculation of simple interest is done on the principle. The mathematical formula for the calculation of simple interest is as follows:A= P. (r/100).n where A: Amount of principle
r: Interest rate as a percentage
n: No. of time periods
Compound Interest
In the case of compound interest, the interest is calculated over a period of time using the following mathematical formula.
Inflation and the interest rate
Since interest is considered the price for borrowed funds, it changes with the change in the value of money. This happens at the time of inflation. The nominal rate of interest is the interest rate that is visible to the customers with no adjustments made with regard to the inflation rate. Hence the mathematical formula used for the calculation of the real rate of interest is given as follows:
i= r+? where i: nominal rate of interest
r: real rate of interest
?: Inflation rate
This above formula is criticised on two grounds:
The interest rate would be the same for all places that have the same inflation rate.The lender is only aware of the prevailing inflation rate , not the expected rate of inflation
This problem of information asymmetry is well tackled with the help of the following formula:
it = rt+1 + ?t+1 + ?
where it : nominal interest rate corresponding to the time when the loan is taken rt+1 : expected real rate of interest over the loan tenure
?t+1 : Expected inflation rate over the loan tenure
? : Level of risk involved
