Basic Concepts, Simple and Compound Interest

Interest rates are very powerful and intriguing mathematical concepts. Our banking and finance sector revolves around these interest rates. One minor change in these rates could have tremendous and astonishing impacts over the economy.

Interest is the amount charged by the lender from the borrower on the principal loan sum. It is basically the cost of renting money. And, the rate at which interest is charged on the principal sum is known as the interest rate.

These concepts are categorized into type of interests

• Simple Interest
• Compound Interest

Simple Interest

Simple Interest because as the name suggests it is simple and comparatively easy to comprehend.

Simple interest is that type of interest which once credited does not earn interest on itself. It remains fixed over time.

The formula to calculate Simple Interest is

SI = {(P x R x T)/ 100}   

Where,

P = Principal Sum (the original loan/ deposited amount)

R = rate of interest (at which the loan is charged)

T = time period (the duration for which money is borrowed/ deposited)

So, if P amount is borrowed at the rate of interest R for T years then the amount to be repaid to the lender will be

A = P + SI

Compound Interest:

This the most usual type of interest that is used in the banking system and economics. In this kind of interest along with one principal further earns interest on it after the completion of 1-time period. Suppose an amount P is deposited in an account or lent to the borrower that pays compound interest at the rate of R% p.a. Then after n years the deposit or loan will accumulate to:

P ( 1 + R/100)ⁿ

Compound Interest when Compounded Half Yearly

Example 2:

Find the compound interest on Rs 8000 for 3/2 years at 10% per annum, interest is payable half-yearly.

Solution: Rate of interest = 10% per annum = 5% per half –year. Time = 3/2 years = 3 half-years

Original principal = Rs 8000.

$$Interestforthefirsthalfyear=\; (\frac{8000\times 5\times \mathrm{1)/}}{100}=420$$

Amount at the end of the first half-year = Rs 8000 +Rs 400 = Rs 8400

Principal for the second half-year = Rs 8400

$$Interestforthesecondhalfyear=\; (\frac{8400\times 5\times \mathrm{1)/}}{100}=420$$

Amount at the end of the second half year = Rs 8400 +Rs 420 = Rs 8820

$$Interestforthethirdhalfyear=\; (\frac{8820\times 5\times \mathrm{1)/}}{100}=Rs441$$

Amount at the end of third half year = Rs 8820 + Rs 441= Rs 9261.

Therefore, compound interest= Rs 9261- Rs 8000 = Rs 1261.

Therefore,

$$\mathrm{Co}mpoundinterest=Rs9261-Rs8000=Rs1261$$