Interest is the extra money paid by institutions like banks or post offices on money deposited (kept) with them. Interest is also paid by people when they borrow money. We already know how to calculate Simple Interest.
The interest paid or charged is never simple . The interest is calculated on the amount of the previous year. this is known as interest compounded or compound Interest (C.I.).
Calculating Compound Interest :
A sum of ` 20,000 is borrowed by Heena for 2 years at an interest of 8% compounded annually. Find the Compound Interest (C.I.) and the amount she has to pay at the end of 2 years.
Aslam asked the teacher whether this means that they should find the interest year by year. The teacher said ‘yes’, and asked him to use the following steps :
1. Find the Simple Interest (S.I.) for one year.
Let the principal for the first year be `P_1`. Here, `P_1` = Rs.20,000
`SI_1` = SI at 8% p.a. for 1st year = Rs.`(20000 xx 8 )/100` = Rs. 1600
2. Then find the amount which will be paid or received. This becomes principal for the next year. Amount at the end of 1st year
=`P_1 + SI_1` = Rs.20000 + Rs.1600
= Rs.21600 = `P_2` (Principal for 2nd year)
3. Again find the interest on this sum for another year.
`SI_2` = SI at 8% p.a.for 2nd year = Rs.`(21600 xx 8 )/100`
4. Find the amount which has to be paid or received at the end of second year.
Amount at the end of 2nd year = `P_2 + SI_2`
= Rs. 21600 + Rs. 1728
= Rs. 23328
Total interest given = Rs. 1600 + Rs. 1728 = Rs. 3328
I = `"PNR"/100`.
In this formula I = Interest, P = Principal, N = Number of years and R = Rate of interest at p.c.p.a.
For more information :
1. Some times the interest is calculated at an interval of six months. For the duration of N years, if rate is R and if the interest to be calculated six monthly then the rate is to be taken as `R/2` and the duration is considered as 2N stages of six months.
2. Many banks charge the compound interest monthly. At that time they take the interest rate as `R/12` monthly and the duration is taken 12 x N stages of months and interest is calculated.
3. Now a days banks calculate compound interest daily.
Calculate the amount and compound interest on Rs 62500 for `1 1/2` years at 8% per annum compounded half yearly.
Calculate the amount and compound interest on Rs 10000 for 1 year at 8% per annum compounded half yearly.
Find the difference between the compound interest and simple interest. On a sum of Rs 50,000 at 10% per annum for 2 years.
Rachana borrowed a certain sum at the rate of 15% per annum. If she paid at the end of two years Rs 1290 as interest compounded annually, find the sum she borrowed.
The interest on a sum of Rs 2000 is being compounded annually at the rate of 4% per annum. Find the period for which the compound interest is Rs 163.20.