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4.6 Interest Calculation:

 

Banks and post offices pay a nominal interest on the balance in SB accounts. The interest % varies from time to time. In the case of Banks it is fixed by Reserve Bank of India and hence it is uniform for all Banks. In the case of Post Office, interest% is fixed by Finance Department of Government of India. It has been 3.5% for many years.

In the case of Banks and also Post Offices, the interest is calculated on the basis of monthly minimum balance maintained between 10th and the last day of each month. But From April 2010, Banks are calculating SB interest on balance held at the end of every day.

 

4.6.1 Interest on Savings Bank Account in Banks:

 

In the case of Banks the interest is calculated monthly but credited to the SB account quarterly or half yearly. Method of finding out monthly minimum balance:

Let us assume that an individual has following balances in the month of February of 2004 in his SB account in a Bank

 

Dates

Account Balance

No of Days with same balance

Balance in single day

On 1st,2nd,3rd,4th,5th

2000

5

      10,000(=2000*5)

On 6th ,7th,8th,9th

2500

4

      10,000(=2500*4)

On 10th

2200

1

      2,200(=2200*1)

On 11th to 20th

3000

10

30,000(=3000*10)

21st to 25th

2600

5

     13,000(=2600*5)

26th to 28th

1400

3

      5,200(=1400*3)

29th

1300

1

     1,300(=1300*1)

Total

29

      71,700

 

The lowest daily balance from 10th to last of day of the month (29th) is Rs 1300.

Hence the interest of 3.5% is paid for February month on Rs 1300 for one month (On Rs39,000(=1300*30) for 1 day),though on many days the account had balance more than this amount. Effective from April 2010, in the banks, SB interest @3.5% is paid on Rs 71,700 for one day, as if this amount is  in the account for just one day.

4.6.1 Problem 1:

Let the monthly minimum balance for April 2006(Minimum daily balance between 10th and 30th in April) be 2000.

Let the monthly minimum balance for May 2006 (Minimum daily balance between 10th and 31st in May) be 2400.

Let the monthly minimum balance for June 2006 (Minimum daily balance between 10th and 30th in June) be 1600.

 

Solution :

 

Since the interest is calculated monthly in every quarter of the year (totally four quarters in a year), the banks use a term called product for easy calculation

 

‘Product’ is defined as sum of the three monthly minimum balances of three months in a quarter.

In the above Problem

Product = 2000+2400+1600= 6000. Interest at the rate of 3.5% is calculated on this product for one month and the amount is credited to the SB account on 1st month of next quarter (i.e. July)

For interest calculation we use the following formula

Interest = P*(N/12)*(R/100)

Where

P = Principal (Product)

N =Period(one month: 1/12 of year)

R = Rate of Interest

Since rate of SB interest is 3.5%

Interest = P*(N/12)*(R/100) = 6000*(1/12)*(3.5/100)= Rs 17.5

This amount of Rs 17.5 is credited to the SB account on 1st day of the next month (i.e. July 2006)

 

In banks instead of using formula each time, they use a ready Reckoner (Pre calculated table of interest for different amount and interest rate) similar to the one given below

 

Principal(Rs.)

Rate@ 3.5%

Per Annum

Rate@ 4%

Per Annum

1

0.0029

0.0033

2

0.0058

0.0067

5,…….

0.0146

0.0167

…….

…….

……

10 ……

0.0292

0.0333

…….

…….

……

100

0.2917

0.3333

…….

…….

……

1000

2.9167

3.3333

2000

5.83333

6.6667

3000

8.7500

10.000

4000

11.667

13.333

5000

14.5833

16.667

10000

29.1667

33.3333

 

 

 

 

In the above Problem 6000 can be split as 5000+1000

From the Ready Reckoner for 3.5% we note that interest for one month, for Rs 5000 it is 14.5833 and for Rs 1000 it is 2.9167

 Interest for 6000 = Interest for 5000+ Interest for 5000 = 14.5833+2.9167 =17.5.

 

Was not this the result we got using the formula?

 

 Schedule for crediting of SB interest in Banks:

Interest for the months of

Interest credit date

January, February, March

On April 1st

April, May, June

On July 1st

July, August, September

On October 1st

October, November, December

On January 1st

 

4.6.1 Problem 2 : The following are extracts  a SB account holder in Karnataka Bank. Check the correctness of SB interest calculated by bank for the quarter (April, May and June 98) if the SB rate of interest is 4%

 

Date

Particulars

Debit(-)

Credit(+)

Balance

1/4/98

Opening

-

 

1500.00

9/4/98

To cheque

300

 

1200.00

10/4/98

By Cash

 

100.00

1300.00

10/4/98

To Cheque

200.00

 

1100.00

1/6/98

By cheque

 

300.00

1400.00

15/6/98

By cash

 

300.00

1700.00

1/7/98

By SB  interest

 

12.00

1712.00

 

Solution:

 

Let us find now the Monthly minimum balance for the three months starting from April 98.

 

No.

Month

Lowest balance

Explanation

1

April’98

1100

On April 10th there were two transactions and the lowest of the two balances is 1100

2

May’98

1100

May did not have any transactions and hence the balance on all days in May was 1100

3

June’98

1400

Rs 300 was deposited  after 10th of June

 

Product

3600

 

 

It is given that rate of interest is 4%

Interest = P*(N/12)*(R/100) = 3600*(1/12)*(4/100) = 12

This amount of SB interest was correctly credited by the bank to the account on 1st July 98, From July onwards; the SB interest credited to the account is also included for monthly SB interest calculation.

 

Note :

Interest earned on a deposit of Rs 5000 for 30 days is equal to interest earned on a deposit of 1,50,000(=5000*30) for one day

(5000*30 days = 150000*1day)

Similarly interest earned on a deposit of Rs5, 000 for 12 months is equal to interest earned on a deposit of Rs.60, 000(=5000*12) for one month.

(5000*12 months = 60000*1 month)

 

4.6.2 Interest on Savings Bank account in Post offices:

 

In post offices also the method of calculating SB interest is same as in Banks but the interest is credited only once a year on 1st of April. The monthly minimum balance in Post office is called ‘Interest bearing balance’ which is the lowest of daily balances between 10th and the last day of any month.

The SB interest can be calculated using the formula or Ready Reckoner

 

4.6.2 Problem 1 :  Madhuri has a post office SB account. The following are extracts of her pass book. Find out the interest which gets credited to her account on 01/04/2000 if rate of SB interest is 4%.

 

Date

Debit(-)

Credit(+)

Balance

1/4/99

-

20.00

20.00

6/5/99

 

275.00

295.00

18/6/99

22.00

 

273.00

26/6/99

 

108.00

381.00

7/7/99

 

113.00

494.00

7/8/99

24.00

 

470.00

12/10/99

17.00

 

453.00

5/11/99

 

130.00

583.00

11/12/99

 

105.00

688.00

8/1/2000

95.00

 

593.00

22/2/2000

210.00

 

383.00

10/3/2000

 

38.00

421.00

 

Solution:

 

Let us find now the ‘Interest bearing balance’ (IBB) for all the 12 months starting from April 99 to March 2000

 

No.

Month

Lowest balance

Explanation

1

April’99

20

 

2

May’99

295

 

3

June’99

273

Rs 108 was deposited after 10th

4

July’99

494

 

5

August’99

470

 

6

September’99

470

There was no deposit or withdrawal in September

7

October’99

453

On 10/10 the balance was 470

8

November’99

583

 

9

December’99

583

Rs 105 was deposited after 10/12

10

January’2000

593

 

11

February’2000

383

 

12

March’2000

421

 

 

Total IBB

5038

 

 

We have seen that

Interest = P*(N/12)*(R/100) = 5038*(1/12)*(4/100)= Rs 16.79

This amount will be credited by post office on 1/04/2000 to the SB account of Madhuri

Exercise : Verify that you will get same interest if you use Ready Reckoner  maintained in post offices for  4% interest (for using ready reckoner,split 5038 as 5000+30+8)

 

4.6.3. Interest on other types of accounts in Banks:

 

What do people do when they receive large amount of money (on retiring from service, on sale of property, .). In some cases they may need that money at a later stage for buying of property. In such cases people normally invest such an amount in Banks for a longer period.

1.  As Cumulative term deposit so that they get the invested amount along with interest at the end of maturity (CTD)

2.  As Fixed deposits for a fixed time so that they can earn interest regularly (FD)

 

4.6.3.1. Cumulative term deposit (CTD)

 

In this scheme a fixed amount is invested for a fixed period. The interest is paid at the end of the maturity period along with initial deposit. This scheme is suitable for those who need money after some time (buying property). The period is normally for few years. The depositor needs to make an application to bank. On payment of initial deposit bank issues a certificate to the deposit holder.

 

Let us look at an example of a CTD issued by Karnataka Bank

 

 

 

Let us understand some important details the above CTD has

 

Circled Number

Details

Entry in the above CTD

1

Name and address of the person

Somayaji, No 97, . . .Bangalore

2

Amount of deposit in Figures  and words

Rs 1,000  One thousand

3

Date of deposit

29-04-2009

4

Period of deposit

one year

5

Interest Rate

8.5%

6

Maturity (Due) Date

(The date on which Amount is payable)

29-04-2010

7

Payable  to whom

Self

8

Type of deposit

Abhyudaya (CTD)

9

Maturity value

1,088

10

Name of branch

Jayanagara

11

Signature of Manager

 

12

Other terms

 

In the above example the depositor gets 1,088 after 1year on an investment 1,000( Thus he gets in all   88 as Interest @8.5%%)

In effect in this scheme the depositor gets interest on interest (called compound interest).

Bank uses either a formula (studied later) or a Ready Reckoner to find the compound interest 

The Ready Reckoner for calculating interest for few quarters @ 9% for different amount is as given below

 

Principal

I Quarter

II Quarter

III Quarter

IV Quarter

100

102.2500

104.5506

106.9030

109.3083

200

204.5000

209.1013

213.8060

218.6167

300

306.7500

313.6519

320.7090

327.9250

….

…..

……

…..

……

         

4.6.3.2. Fixed Deposit (FD)

 

In this scheme a fixed amount is invested for a fixed period and the interest is paid regularly (quarterly). This scheme is suitable for those who need money regular interest for meeting their monthly expenses. (Retired people). The period can vary from few days to few years (say 7 days to 3 years)

The depositor needs to make an application to bank. On payment of initial deposit bank issues a certificate to the deposit holder which is similar to format of CTD.

The interest is calculated using the formula:

Simple Interest  = P*N*(R/100)

Where

P = Initial deposit (Principal)

N = Period (Term) of Deposit in years

R = Rate of Interest

 

4.6.3.3. Recurring Deposit (RD)

 

In this scheme, a depositor opens an account with the bank agreeing to pay a fixed amount every month for few months (three to six years)

After the maturity period, the bank pays back sum of his all monthly installment amounts and also the compounded interest. This scheme is useful for those who are in a position to save a fixed amount every month(salaried employees, fixed wage earner, shop owners…). RD accounts is helpful for those who need fairly large amount after few years for buying items( vehicles, farm equipments, ) and who  have regular monthly income  and can save a fixed amount every month. Normally

Banks use a Ready Reckoner to find the amount payable at the end of maturity period.

The Ready Reckoner for repayment amount for few months (6,12,24,36)  for different Interest rates(6,8,10) for a  monthly installment amount Rs 100 is given below.

 

Interest Rate

6 months

…..

12 months

….

24 Months

36 months

……

6%

610.5350

 

1239.5234

 

25555.1084

3951.4233

 

……

 

 

 

 

 

 

 

8%

614.0622

 

1252.9326

 

2609.1471

4077.1572

 

….

 

 

 

 

 

 

 

….

 

 

 

 

 

 

 

10%

617.5972

 

1266.4603

 

2664.3955

4207.4544

 

….

…..

 

……

 

…..

……

 


Note : Banks prepare  above  Ready Reckoner after applying mathematical formula similar to

 

Maturity amount= P*(1+(R/100)) N + P*(1+(R/100)) N-1+ P*(1+(R/100)) N-2 + . . .  P*(1+(R/100)) 1

 

Where P is installment amount per month. N = Number of months for which RD is opened, R= Rate of interest per month.

 

4.6.3     Problem 1 : If  Nanda  saves every month 50 Rupees for three years, find out how much she gets at the end of three years  @ 8% interest and also the interest part in that amount.

 

Solution :  

 

We find that for a monthly installment of Rs 50 @ 8% for 36months, the amount mentioned in the above ready Reckoner is 4077.15(rounded)

Hence at the end of 36 months she will receive Rs. 4077.15.

Since her monthly installment is Rs 50 and not 100

She will receive 4077.15*50/100 = 2038.58(rounded)

What was the sum of all her monthly installments?

Sum of monthly installment = Monthly installment*Number of months = 50*36 = 1800

 Total interest received = Amount received on maturity – Sum of monthly installments = 2038.58-1800 = 238.58.

 

Note:

1. In the above case rate of interest per month is 8/12 (Rate for 12 month is 8%)

2. The interest % increases with the increase in period of deposit. The interest % offered by various banks is almost same.

You can visit the internet sites of the banks to know the applicable interest % for various periods at any time.

 

No.

Features

Recurring Deposit(RD)

Fixed Deposit(FD)

Cumulative Term Deposit(CTD)

1

Opened by

Individuals/ Business man or Companies

2

Period of deposit

Fixed number of months

Fixed number of days

3

Amount of deposit

Fixed amount every month

Fixed amount in the beginning itself

4

Refund of deposit

At the end of maturity period

5

Payment of interest

At the end of maturity period along with deposited amount

Every month/3 months/6 months/year

At the end of maturity period along with initial deposit

6

Useful for/when

For people with fixed income

When in receipt/need of lump sum amount

7

Minimum deposit

 

Minimum amount varies from bank to bank

8

Payment of amount

Credited to account or paid by cheque

 

4.6.3.4. Bank loans

 

When banks collect deposits from public they need to find a way for disbursement (payments)  of large amount of money with them. This they do so by giving loans to individuals, companies, businessmen. Like the way banks  give interest to depositors on deposits, they collect interest from borrowers of loans.

The loans can be categorized as

1.  Demand loans

These are loans repayable on demand. The borrower executes an agreement with the bank, promising the Bank to repay the loan at the end of loan period.

Normally loan period is of short duration less than 3 years. This type of loan is availed by individuals and  ????

2.  Term loans

These are similar to demand loans with the difference that term of loan is more than 36 months. This type of loan is availed by individuals and  ???

In the case of above two types of loans, interest is calculated on the loan outstanding on a monthly balance basis. Interest is collected (debited) quarterly. Banks calculate daily products and on the sum of these daily products, they find the interest.

 

4.6.3.5. Overdrafts

 

This is strictly is not a loan but a financial arrangement of borrowing of amount for few days at a time. In this type of arrangement the current account holder is allowed by the bank to draw more than the balance amount in his account. The borrower and the bank agree on a upper limit. The borrower can not draw more than this limit. Overdraft facility is used mostly by traders and small businessmen when they need extra money for a short period.

 

In the case of overdrafts, interest is calculated on the loan amount outstanding at the close of day on a day to day basis. Interest is collected (debited) quarterly

 

Calculation of interest on loans

Daily product = balance * number of days  the same balance was outstanding

Interest = (Sum of daily products* interest rate)/(100*365)

4.6.3 Problem 2:  A person has taken  a loan 1,00,000 on 15/1/01 at 12% He repays 25,000 on 18/2/01 and Rs 10,000 on 16/03/01 and 40,000 on 28/4/01. The loan was closed on 16/5/01. Calculate the interest compounded quarterly.

 

Solution :

We first need to find the balance amount for each of the days from 15/1/01(Loan taken date) to 28/4/01(Loan repayment date) as follows

 

Loan amount balance

Remarks

From date

To  Date

Number of days

Daily product =

Balance*Number of days

100000

Initial loan

15/01/01

17/02/01

34(=17+17)

3400000=100000*34

75000

Balance reduced on 18/02/01 because of repayment of 25000

18/02/01

15/03/01

26(=11+15)

1950000= 75000*26

65000

Balance reduced on 16/03/01 because of next repayment of 10000

16/03/01

31/03/01

16

1040000=65000*16

Since the interest is compounded quarterly, we need to calculate the interest up to the calendar quarter ending 31/03/01.

 

Sum of daily products =6390000(=3400000+1950000+1040000)

Interest = (Sum of daily products* Interest rate)/(100*365) = (6390000*12)/(100*365)= 2100.82 ( rounded to 2100)

Thus  the amount  outstanding as on 01/04/01 is 67100 ( = 65000 loan + interest of Rs 2100)

67100

Balance increased by  interest of Rs 2100.

01/04/01

27/04/01

27

1811700 =67100*27

25000

Balance reduced on 28/04/01 because of repayment of 40000

28/04/01

15/05/01

18(=3+15)

 450000=25000*18

0

Loan closed on 16/05/01

 

 

 

 

 

 

Sum of daily products =2261700(=1811700+450000)

Interest = Sum of daily products* Interest rate/100*365 = (2261700*12)/(100*365) = 743.57

 

Thus the total interest paid = 2100.82+743.57 = 2844.39

 

4.6 Summary of learning

 

 

No

Points learnt

1

Method of calculation of  interest on SB account in Banks and Post offices

2

Method of calculation of  interest on loans

 

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