Time preferences, value and interest Time preference Time value of money Simple and compound interest Determination of Market interest rate Market equilibrium for interest rate Real rate of interest

Time preference Time preference between present and future is the basis for making economic decisions. Individuals with a positive time preference value units of current consumption or income more than accruing in future. Discount rate: rate at which the future benefits and costs are discounted because of time preference Discounting: calculation of present value of a future payment Compounding = Future value of a payment or series of payment

Time value of money In simple word’s Interest is the rental price of money i.e., the price paid for the use of a specific sum of money for a specified period of time – because future always carry less weight than the present The rate of interest gives an individuals time preference if an individual’s time preference is nil, the individual is indifferent for receiving money now and in future. But in real life individual’s time preference is not nil and often carries higher value under different circumstances such as the individual’s age, preference, priority, risk associated with dealings etc.

Simple Interest Simple interest is calculated on the original principal only. Accumulated interest from prior periods is not used in calculations for the following periods. Simple interest is normally used for a single period of less than a year. Simple Interest = p * i * n where: p = principal (original amount borrowed or loaned) i = interest rate for one period n = number of periods Example: You borrow $10,000 for 3 years at 5% simple annual interest. interest = p * i * n = 10,000 *.05 * 3 = 1,500 Example 2: You borrow $10,000 for 60 days at 5% simple interest per year (assume a 365 day year). interest = p * i * n = 10,000 *.05 * (60/365) =

Compound Interest Compound interest is calculated each period on the original principal and all interest accumulated during past periods. Although the interest may be stated as a yearly rate, the compounding periods can be yearly, semiannually, quarterly, or even continuously. You can think of compound interest as a series of back-to-back simple interest contracts. The interest earned in each period is added to the principal of the previous period to become the principal for the next period. For example, you borrow $10,000 for three years at 5% annual interest compounded annually:

Compound interest contd interest year 1 = p * i * n = 10,000 *.05 * 1 = 500 interest year 2 = (p2 = p1 + i1) * i * n = (10, ) *.05 * 1 = 525 interest year 3 = (p3 = p2 + i2) * i * n = (10, ) *.05 * 1 = Total interest earned over the three years = = 1, Compare this to 1,500 earned over the same number of years using simple interest. We use the formula: P * (1+i) n to calculate the compounded amount.

Comparing interests The power of compounding can have an astonishing effect on the accumulation of wealth. The next table shows the results of making a one-time investment of $10,000 for 30 years using 12% simple interest, and 12% interest compounded yearly and quarterly.

Comparing interests

Attractive offers If Laxmi Bank comes with an attractive offer for fortnight compounding in the above case then the amount at the end of the period will be Rs Global Bank with the most lucrative offer of daily compounding, try to find out the compounded amount after 30 years based on the fore given example.

Market rate of interest The market rate of interest is the rate at which an investor actually pays to the lender for the use of money so borrowed or the lender actually receives from the borrower for making the sum available to him for a specific period of time. The market rate of interest reflects the opportunity cost of capital. Generally, there are lending and borrowing rates. The later is usually slightly higher than the former rate to cover the administrative expenses of financing institutions. Various lending and borrowing rates occur in a market due to the market imperfection and risk factor. Removal of risk factor from the market rate of interest gives the economic rate of interest.

Determination of market rate of interest Demand and supply of capital (total capital = NRs 60,000) Rate of return (%) Demand of capital (Rs)Supply of Capital (Rs) 1050,00010, ,00020, , ,00040, ,00050,000

Determination of Rate of Interest AB Excess supply C D d d1d1 s s1s1 Excess demand Interest rate Y q r Market Equilibrium X

Real rate of interest Real rate of interest is the nominal market interest rate corrected for inflation. Real rate of interest (r) is derived from market rate as follows: r = (1+R) / (1+P) - 1 Where, R is the market rate and P is the rate of inflation or price rise If R = 20% and P = 10% then r = (1.2/1.1) – 1 = = *100 = 9.09%

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