Friday, 11 March 2016

EMI

EQUATED MONTHLY INSTALMENT

It is a fixed payment made by a borrower to a lender.
It covers principal and interest.
Interest is payable only on outstanding loan amount.

EMI = (P*r) (1+r)n
                  (1+r)n-1
Where:
P = Principal
r = rate of interest per instalment period
n = number of instalments in the tenure

Question.1
Ram took a loan for Rs. 1,00,000/- at an interest rate of 12% per annum for a period of 12 months. Find out the EMI and prepare a schedule of repayments.

Solution:

DATA

Principal (P)
1.00.000
Interest rate per annum
0.12
Number of instalments (n)
12
Rate of interest per instalment period (r )= 0.12/12
0.01



EMI = (1,00,000 * 0.01) (1+0.01)12
                (1+0.01)12- 1                         
        = 1,000 * (1.01)12
            (1.01)12- 1

        = 1,000 * 1.126825
           1.126825 -  1

        = 1,000 * 1.126825
           0.126825

        = 1126.825
         0.126825

        = Rs. 8,885


HOW TO CALCULATE EQUATED MONTHLY INSTALMENTS (EMI) IN MICROSOFT EXCEL


The function PMT is used to calculate EMI in MS Excel. It requires 5 inputs. They are

INPUT
MEANING
VALUES TO BE GIVEN IN MS EXCEL FOR THE ABOVE EXAMPLE



Rate
Rate means interest rate per instalment
0.12/12
Nper
Nper means total number of instalments of loan
12
pv
Present Value or the total amount that a series of future payments is worth now
1,00,000
fv
Future value or cash balance that you want to achieve after the last payment is made. If future value is omitted it is assumed as zero
0
type
Type means when payments are due. Type zero or omitted means the payments are due at the end of the period. Type one means payments are due at the beginning of the period
0


The function IPMT is used to calculate Interest in MS Excel. It requires 5 inputs. They are

INPUT
MEANING
VALUES TO BE GIVEN IN MS EXCEL FOR THE ABOVE EXAMPLE



Rate
Rate means interest rate per instalment
0.12/12
Per
Per is the period for which you want to find the interest. It means one instalment. Hence give it 1.
1
Nper
Nper means total number of instalments of loan
12
pv
Present Value or the total amount that a series of future payments is worth now (Principal)
1,00,000
fv
Future value or cash balance that you want to achieve after the last payment is made. If future value is omitted it is assumed as zero
0


 Schedule of Repayment

MONTH   LOAN                           EMI       INTEREST  PRINCIPAL   LOAN AT END
             OUTSTANDING
             AT THE
             BEGINNING
Jan-15
                                  100,000
        8,885
        1,000
        7,885
                          92,115
Feb-15
                                   92,115
        8,885
           921
        7,964
                          84,151
Mar-15
                                    84,151
        8,885
           842
        8,043
                          76,108
Apr-15
                                    76,108
        8,885
           761
        8,124
                          67,984
May-15
                                    67,984
        8,885
           680
        8,205
                          59,779
Jun-15
                                    59,779
        8,885
           598
        8,287
                          51,492
Jul-15
                                    51,492
        8,885
           515
        8,370
                          43,122
Aug-15
                                    43,122
        8,885
           431
        8,454
                          34,668
Sep-15
                                    34,668
        8,885
           347
        8,538
                          26,130
Oct-15
                                    26,130
        8,885
           261
        8,624
                          17,507
Nov-15
                                    17,507
        8,885
           175
        8,710
                             8,797
Dec-15
                                      8,797
        8,885
              88
        8,797
                                     0



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Thursday, 10 March 2016

COMPOUND INTEREST

COMPOUND INTEREST

·          Interest is payable periodically on the principal and accumulated part of interest.
More interest can be earned by increasing the number of compounding per year.
The time period between which the interest is added to the account is called the compounding period.

Formula

Accumulated Amount (A) = P (1+r/n)nt

Where :
P = Principal
r = Interest rate per annum in percentage expressed as fraction (6% =  0.06)
n = Number of times per year that interest is compounded
t = Number of years invested
A = Accumulated amount (Principal + Interest)

Question 1
Raju invested Rs 10,000 in a fixed deposit for 1 year at a compound interest rate of 6% per annum. Find out the accumulated amount after one year if
A.    Interest is compounded annually
B.    Interest is compounded semi annually
C.    Interest is compounded quarterly
D.   Interest is compounded monthly
E.    Interest is compounded weekly
Which method of compounding is advantageous?

Option A
DATA

Principal
10,000
Rate
0.06
Time
1 year
Compounding
Annually

A = P (1+r/n)nt
   = 10,000 * (1+0.06/1)1*1
   = 10,000 * (1.06)
   = Rs. 10,600

Option B
DATA

Principal
10,000
Rate
0.06
Time
1 year
Compounding
Semi Annually

A = P (1+r/n)nt
   = 10,000 * (1+0.06/2)2*1
   = 10,000 * (1+0.03)2
   = 10,000 * (1.03)2
   = 10,000 * 1.03 * 1.03
   = 10,000 * 1.0609
   = Rs. 10,609

Option C
DATA

Principal
10,000
Rate
0.06
Time
1 year
Compounding
Quaterly

A = P (1+r/n)nt
   = 10,000 * (1+0.06/4)4*1
   = 10,000 * (1+0.015)4
   = 10,000 * (1.015)4
   = 10,000 * 1.015 * 1.015 * 1.015 * 1.015
   = 10,000 * 1.0613
   = Rs. 10,613

Option D
DATA

Principal
10,000
Rate
0.06
Time
1 year
Compounding
Monthly

A = P (1+r/n)nt
   = 10,000 * (1+0.06/12)12*1
   = 10,000 * (1+0.005)12
   = 10,000 * (1.005)12
   = 10,000 * 1.0616
   = Rs. 10,616

Option E
DATA

Principal
10,000
Rate
0.06
Time
1 year
Compounding
Weekly

A = P (1+r/n)nt
   = 10,000 * (1+0.06/52)52*1
   = 10,000 * (1+0.0011)52
   = 10,000 * (1.00115384615)52
   = 10,000 * 1.0618
   = Rs. 10,618


SUMMARY

OPTION
COMPOUNDING PERIOD
ACCUMULATED AMOUNT


Rs.
A
Annually
10,600
B
Semi Annually
10,609
C
Quarterly
10,613
D
Monthly
10,616
E
Weekly
10,618


Option E is advantageous because more interest is earned by increasing the compounding periods per year.
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