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8/8/2019 16.Interest Calculation
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Interest Calculation
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Objectives
On completing this session we will be able too understand the concept of interest rate,
o state different types of interest rates and itsapplications in banking situations.
o compute the interest on savings account deposits
o compute the interest on fixed deposito compute EMI and prepare the amortization
schedule
o computation of interest for overdraft on dailyproducts method
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Concept of Interest Rate
Interest is a fee paid by the borrower for the use ofmoney he does not own and is the return for thelender.
One of the factors of production is capital
Its cost is interest comparable to rent on land,
salary on labor etc. Compensation for the owner of funds to part with it
for some time
Interest rates are normally expressed as apercentage over a period of one year
Rate could vary over a period of time and for thesame period could vary with time
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Fixed Interest Rates
Fixed interest rate does not change during thetenure.
When fixed interest rate should be opted?
Is fixed interest rate fixed throughout the loan
tenure?
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Floating interest rate
Banks offer deposit with fixed rate of interest andfloating rate of interest for a maturity periods ranging
from 7 days to 10 days.
Banks also offer loans with fixed rate of interest and
floating rate of interest.
Which is better in the scenario of increasing or
decreasing interest rates?
Is it true that what is better for depositor is not so for
borrower and vice versa?
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For the Depositor
Fixed interestrate
Floating interestrate
Interest rate
raising
Interest rate
falling
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Floating interest rate
Mr. Divakar wants to deposit Rs.100000 and he hastwo option i.e. fixed rate and floating rate. Fixed
interest on that date is 5.5% and floating rate on that
date is 5.23%. He opted for floating rate. The floating
rates for the next three quarters are 5.73, 6.18 and
6.02 respectively.
o Find the interest earned by the Divakar for one year.
o Has he benefited by choosing the floating rate.
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Floating interest rate
The interest earned by Divakar iso I Quarter = (100000x5.23x3)/(100x12)=1307.50
o II Quarter= (100000x5.73x3)/(100x12)=1432.50
o III quarter= (100000x6.18x3)/(100x12)=1545.00
o IV quarter= (100000x6.02x3)/(100x12)=1505.005790.00
If he goes for fixed interest rate, he earns an interest
of
o (100000x5.5x1)/100 = Rs.5500.
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Calculation of interest on savings
accounts
Balances in the account varies day to day dependingon the debit and credit in the account.
So, which balance should be consider for the
calculation of interest?
According to the RBI guidelines, the interest for aparticular month is computed on the minimum
balance between the 10th day and the last day of the
month.
WHY 10th OF MONTH?
Will deposit after the 10th day of month earn interest?
Though the interest is computed month wise, it is
usually credited to the account every six months.
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Example
A page from the pass book of Mr. Chandrus ICICI savings
bank account is as follows:
Date Particulars Debit Credit Balance
1-3-07 BF 2630.50
20-5-07 By Cash 1050.00 3680.50
25-5-07 To self 200.00 3480.50
14-7-07 By Cash 2000.00 5480.50
17-8-07 By Cash 1700.00 7180.50
21-8-07 To cheque No.312 5102.00 2078.50
Assuming that the interest is credited at the end of the
March and September every year and rate of interest is
3.5% per annum; compute the interest at the end of
September 07.
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Solution
Minimum balance for the month of Apr 2007 = 2630.50
Minimum balance for the month of May 2007 = 2630.00
Minimum balance for the month of Jun 2007 = 3480.50
Minimum balance for the month of July 2007 = 3480.50
Minimum balance for the month of Aug 2007 = 3480.50
Minimum balance for the month of Sep 2007 = 2078.50
17781.00
Now Rs.17781 is treated as the principal forONE MONTH
interest calculation.
51.86Rs.10012
5.3117781
100
PTRInterest !
v
vv
!!
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Savings Accounts
Is there any prescription to maintain a minimumbalance in savings account?
Yes. Differs from bank to bank and types of savings
account
Does it mean that a savings account balance cannever be zero?
No. The depositor has maintain the average quarterly
minimum balance.
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Calculation of interest on term deposit
In the fixed deposit, the investor has two options.
They are
o Withdrawal of interest periodically say quarterly, semi-
annually and annually.
o Reinvest of interest and get along with principal
amount on maturity According to the guidelines of RBI, in both the above
cases the interest will be calculated on the basis of
quarterly compounding.
Usually interest is payable once in quarter. An
investor can opt for monthly withdrawing of interest
but he/she will get little less interest because it is
discounted.
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Example
Mr. Kartik deposited Rs.10000 in a fixed deposit for aperiod of three years. Calculate the amount of
interest you can withdraw if you decided to withdraw
interest
o Yearly
o Semi-annually
o Quarterly
o Monthly
Suppose you decided to withdraw interest at the time
of maturity. What is the interest you receive onmaturity?
Assume interest rate is 9%p.a.
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Solution
Annually
Semiannually
Quarterly
Monthly
At the end of the five years
83.930100004
09.0110000-k)(1Interest
4
n
!
!!
06.455100004
09.0110000-k)(1Interest
2
n !
!!
225100004
09.0110000-k)(1Interest
1
n !
!!
306010000409.0110000-k)(1Interest
12
n!
!!
70.73100004
09.0110000-k)(1Interest
1/3
n !
!!
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Loan repayment methods
What are the possible modes of repayment of a termloan?
o Monthly repayment
o Bi monthly repayment
oQuarterly repayment
o Semi-annually repayment
o Annual repayments
o Structured repayments
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Equated Monthly Installment
Earlier bank used to recover principle amount equalmonthly installment and interest every quarterly. In
this method interest would be high at initial period
and borrower found difficult to repay.
This leads to the evolution of EMI.
A method of making the installment equal throughout
More appealing to customers
Knows precise amount to be kept separately every
month for repayment; personal budgeting easier
As time passes, repaying capacity normally increases
and hence repayment amount need not to decrease
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Calculation ofEMI & Amortization
.o Where,
EMI = Equated Monthly Installment
L= Loan amount (Also Present Value)
n= period in terms of months
k = interest rate per month i.e. annual rate/12
Amortization is the split of EMI into the principal and
interest component.
.
.
-
! 1)k1(
)k1(k
LEMI n
n
yearpertinstallmenofNumber
kXBalanceBeginningEMIinamountInterest !
EMIinamountInterest-EMIEMIinamountPrincipal !
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Example
Mr. Mathew has taken a ICICI personal loan of300000 which is repayable in 1 year with EMI. If the
rate of interest is 12%, what is the EMI? Also prepare
amortization table.
266591268.0
1268.130001).011(
)1.1(1)300000x0.0(I 12
12
!
-
!
-
!
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Amortization schedule
Month
Opening
Principal EMI Interest Principal
Closing
Principal
1 300000 26659 3000 23659 276341
2 276341 26659 2763 23896 252445
3 252445 26659 2524 24135 228310
4 228310 26659 2283 24376 203934
5 203
934
26659 203
9 24
6201
79314
6 179314 26659 1793 24866 154448
7 154448 26659 1544 25115 129333
8 129333 26659 1293 25366 103967
9 103967 26659 1040 25619 78348
10 78348 26659 783 25876 5247211 52472 26659 525 26134 26338
12 26338 26659 263 26396 -58*
*Rs.-58 is because of ignorance of decimal part of EMI
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Flexibilities in EMI mode of repayment
Step down scheme Step up scheme
Bulk repayment
Advance EMI
Subvention Moratorium
Loan reschedulement
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Other Concepts
Non-Amortizing Loano A type of loan in which payments on the principal are
not made, while interest payments or minimum
payments are made regularly. As a result, the value of
principal does not decrease at all over the life of the
loan. The principal is then paid as a lump sum atthe maturity of the loan.
Loans with varying repayments, increasing
repayments, step up repayments
Structuring to customers convenience Concept of reverse mortgage how it involves EMI
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Interest on overdrafts
Calculation of interest on reducing balance Can it be on original loan amount?
Concept of product
Its importance in case of varying balances e.g.operative loan account, loan with frequent
repayments, overdraft, cash credit etc. The following formula can be used under daily
product methodo Amount outstanding x Rate of interest x Number of
days amount outstanding/365
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Example
A page from the pass book of Bhagwan Traders Co.s currentaccount is given below. Assume bank overdraft limit is
Rs.50000 and rate of interest is 10%.
Date Particulars Debit Credit Balance
1-1-07 BF 20000
2-1-07 To cheque No.12 35000 (15000)
10-1-07 By cheque No.31 25000 10000
14-1-07 To cheque No.45 60000 (50000)
17-1-07 By Cash 32000 (18000)
25-1-07 To cash 22000 (40000)
28-1-07 By cheque No.32 42000 2000
Calculate the interest on overdraft for the month of January
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Solution
Interest Calculation15000 x 10/100 x 8/365 = 32.90
32000 x 10/100 x 3/365 = 26.30
18000 x 10/100 x 8/365 = 39.50
40000 x 10/100 x 3/365 = 32.90Total Interest 131.50
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Solution
Another way of calculating interest is
Rs.15000 used for only 8 days = 15000X8 =120000
Rs. 32000 used for only 3 days = 32000X3 = 96000
Rs.18000 used for only 8 days = 18000X8 =144000
Rs. 40000 used for only 3 days = 40000X3 =120000
480000
Now Rs.480000 is treated as the loan lent forONE DAY
for interest calculation.
131.50s.100365
101480000100TInterest !v
vv!!