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 used to be  fixed by Reserve Bank of India and hence it was  uniform for all Banks. Now banks are free to decide their own interest rates on SB accounts and it varies from 4%. Some banks pay as high as 7%  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  Post Offices, the interest is calculated on the basis of monthly minimum balance maintained between 10th and the last day of each month. However, 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 interest calculation:

Let us assume that an individual has following balances in the month of February of 2015 in his SB account in a Bank

 Dates Account Balance No of Days with same balance Equivalent Balance held in 1 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

Effective from April 2010, in the banks, SB interest is paid on Rs 71,700 for one day, as if this amount is  in the account for only one day.

4.6.1 Problem 1: Find SB interest @4% in case of a account holder having below mentioned balances:

The balance for April 2015 on all the days of the month  be 2000.

The balance for May 2015 all the days of the month  be  2400.

The balance for June 2015 all the days of the month  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

‘Daily Product’ is defined as the balance at the end of each day.

'Product'  is balance at the end of the day* Number of days that balance is held.

In the above Problem

Product = 2000*30+2400*31+1600*30= 1,82,400. Interest at the rate of 4% is calculated on this product for one day 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*(1/365)*(R/100)

Where

P = Principal (Product)

N =Period(one day: 1/365 of year)

R = Rate of Interest

Since rate of SB interest is 4%

Interest = P*(1/365)*(R/100) = 182400*(1/365)*(4/100)= Rs 19.9

This amount of Rs 19.9 is credited to the SB account on 1st day of the next month (i.e. July 2006)

Schedule for crediting of SB interest in Banks normally is :

 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 2015) if the SB rate of interest is 5%

 Date Particulars Debit(-) Credit(+) Balance 1/4/2015 Opening - 1500.00 9/4/2015 To cheque 300 1200.00 10/4/2015 By Cash 100.00 1300.00 10/4/2015 To Cheque 200.00 1100.00 1/6/2015 By cheque 300.00 1400.00 15/6/2015 By cash 300.00 1700.00 1/7/2015 By SB  interest 16.05 1716.05

Solution:

Let us find now the  product  for the three months starting from April 2015.

 No. Month product Explanation 1 April 2015 1500*8= 12000 1200*1=   1200 1100*21=23100 Up to 8th balance was 1500. 8th balance was 1200 On April 10th there were two transactions and the closing  balance was 1100 and it was same then for full month of April 2 May 2015 1100*31=34100 May did not have any transactions and hence the balance on all 31 days in May was 1100 3 June 2015 1400*14=19600 1700*16=27200 Up to 14th , balance was 1400 and then for next 16 days it was 1700 Total 117200

It is given that rate of interest is 5% Interest = P*(1/365)*(R/100) = 117200*(1/365)*(5/100)=  16.05

This amount of SB interest was correctly credited by the bank to the account on 1st July 2015, From July onwards; the SB interest credited to the account is also included for monthly SB interest calculation.

Note :

1.      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)

2.      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

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