16.interest calculation

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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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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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!!

16.interest calculation

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