☛ GETTING STARTED
☛ Interest: An additional amount paid back by a borrower to the lender for using the latter’s money.
☛ The two common ways of calculating the interest are – simple interest and compound interest
☛ This is a direct application of the Unitary method.
☛ The amount given out on loan is known as ‘Principal’
☛ Amount paid as interest for every Rs.100 borrowed for a year is known as ‘rate of interest’ and is expressed as ‘p.c.p.a’ ( Per cent per annum)
Eg. Ram borrowed Rs.10,000 from Manilal under the condition that Ram has to pay an interest at 10 per cent per annum. Ram being naive, did not understand the meaning of it.
Manilal further explains: For every Rs.100 borrowed for a year , Ram has to pay Rs. 10.
Ram calculates that for one year of borrowing, he has to pay Rs. 10000*10/100.
= Rs. 1000
SI for 1 year of borrowing is PR/100
Ram says, I will repay the amount after 2 years.
Manilal replies, “My terms are fixed. You will incur interest for both the years then”
Ram calculates again. The interest was Rs.1000 for 1 year.
For the second year also, the interest will be Rs.1000
So, it should be
Rs. 1000 x 2
=Rs.2000 for 2 years
If it was PR/100 for 1 year, it would be PNR /100 where N is the number of years and R is rate of interest
SI for any given sum = PNR/100
It is to remembered that the interest incurred every year for the borrowed sum will be the same, which is PR/100
☛ It is the interest paid on both the borrowed capital as well as the interest accrued for the previous interest generated on the sum
Calculate the compound interest for Rs. 2400 @ 8% for 2 years.
For the 1 st year:
8/100 x 2400
= Rs. 192 (Since there is no previous interest )
For the 2nd year:
8/100 x (2400+192) (Since the interest for 1st year is Rs.192 )
Hence the CI for 2 years is (Rs. 192 + Rs.207.36) = Rs.399.36
FORMULA FOR COMPOUND INTEREST
Note: CI and SI are equal for the first year. In all other cases, CI is always greater than SI.
When number of year < 2, it is better to use the concepts as it is less time consuming
Compounding Half yearly and Quarterly
For Compounding Half-Yearly,
Similarly, for Compounding Quarterly,
Finding the CI when N (no. of years) is in mixed fraction
Step 1 : Find the Accrued amount for the integer number of years
Step 2: Find SI for the remaining fraction number of years using the amount obtained in Step 1 as Principal
Step 3: Add the SI generated in Step 2 to the amount generated in Step 1 and subtract the Principal
Eg. Find the CI for Rs. 2500 lent out at 10% CI for 7/2 years
P= 2500; R = 10% ; N = 7/2
Amount Matured in 3 years
= 2500 x (11/10)3
Find SI for 1/2 years using Rs.3327.5 as principal.
SI for 1/2 year
= 3327.5 x 0.5 x 10/100
= Rs. 116.375
Total Amount to be repaid at end of 7/2 years
CI for 7/2 years
=3443.875 – 2500