SIMPLE & COMPOUND INTEREST

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☛ 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

                     SIMPLE 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)

Let us consider an example for this:

 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

 So, generalizing,

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

 

 COMPOUND INTEREST

☛ It is the interest paid on both the borrowed capital as well as the interest accrued for the previous interest generated on the sum

 

Let us take an example

Calculate the compound interest for Rs. 2400 @ 8% for 2 years.
Soln:
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 )

=Rs. 207.36

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.

TIP:

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,

R’= R/2

N’= 2N

Similarly, for Compounding Quarterly,

R’= R/4

N’= 4N

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

Soln:

P= 2500; R = 10% ; N = 7/2

Step 1:

Amount Matured in 3 years

= 2500 x (11/10)3

= Rs.3327.5

 

Step 2:

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

 

Step 3:

Total Amount to be repaid at end of 7/2 years 

=Rs.3327.5+116.375

=Rs. 3443.875

CI for 7/2 years

= 116.375+3327.5-2500

=3443.875 – 2500

=Rs. 943.875

PRACTICE PROBLEMS

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Created on By venkateshj

Simple & Compound Interest - Practice problems

1 / 22

In how many months will a sum of Rs.25000 at 6% p.a. rate of simple interest yield an interest of Rs.6,625?

2 / 22

What sum will fetch a simple interest of Rs.17280 in seven and a half years at 4% p.a. rate of interest?

3 / 22

What sum will yield an interest of Rs.427 in seven years at 8% p.a. simple interest?

4 / 22

The simple interest for the second year on a certain sum at a certain rate of interest is Rs.224. Find the sum of the interests accrued on it for the 12th and 20th years

5 / 22

Rs.6500 is invested for two years under simple interest at 4% p.a. Find the interest earned

6 / 22

Find the sum of the present values of the payments received at 10% p.a. under compound interest, interest being compounded annually, if Rs.4950 and Rs.6050 are received at the end of the first year and second year respectively.

7 / 22

Gopi borrowed Rs.8400 at 10% p.a. under compound interest, interest being compounded annually. If he has to repay this in two equal annual installments, find the value of each installment.

8 / 22

Girish borrowed Rs.25000 at 10% p.a. under compound interest, interest being compounded annually. He repaid Rs.15000 at the end of the first year. Find the amount he must repay at the end of the second year to clear the loan.

9 / 22

The compound interest on a certain sum for the 2nd year and the 3rd year are Rs.3456 and Rs.3732.48 respectively. Find the sum and the rate of interest.

10 / 22

The compound interest and the simple interest on a sum at certain rate of interest for 2 years are Rs.3870 and Rs.3600 respectively. Find the rate of interest.

11 / 22

A sum amounts to Rs.30250 in two years and to Rs.33275 in three years under compound interest, interest being compounded annually. Find the sum

12 / 22

A sum amounts to Rs.31360 in two years and to Rs.35123.2 in three years under compound interest, interest being compounded annually. Find the rate of interest.

13 / 22

The interest on a sum is compounded every 4 months. If the rate of interest is 30% p.a., find the effective rate of interest per annum.

14 / 22

Find the value that Rs.4000 will amount to in 2 years at 20% p.a., interest being compounded half yearly.

15 / 22

If Rs.6000 is lent at 10%p.a, interest being compounded annually, find the interest for the fourth year.

16 / 22

If Rs. 8000 is lent at 10% p.a simple interest, find the interest for the fourth year.

17 / 22

A sum doubles in 4 years under compound interest at a certain rate of interest, interest being compounded annually. Find the time it would take to become 8 times itself.

18 / 22

If a sum doubles in 3 years under simple interest, find the time that it would take to become 4 times itself at the same rate of interest.

19 / 22

Find the sum that would amount to Rs.7920 under simple interest in 4 years at 8% p.a.

20 / 22

Find the simple interest on a sum of Rs.2000 at 8% p.a. for 5 years.

21 / 22

A sum of Rs.6000 becomes Rs.6960 in 2 years under simple interest. In how many years will Rs.4000 become Rs.5280 under simple interest at the same rate of interest?

22 / 22

Find the value that Rs.3200 would amount to under compound interest at 10% p.a., interest being compounded annually in 2 years.

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