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
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 |
|
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, . . . |
|
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 |