time value of money

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TIME VALUE OF MONEY
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WHY TIME FACTOR IS IMPORTANT IN TIME VALUE OF
MONEY?

• In general, people prefers current consumption
  than to future consumption.
• Money (capital) can be employed productively to
  generate positive return.
• E.g.- Investment of 1rupee today would grow
  to (1r) after a year.
• (r Rate of return)
• In the period of inflation a rupee today
  represents a greater deal than a rupee year ahead.

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Concept to be clear

• Present Value
• - Simple Interest
• - Compound Interest
• Future Value
• - Simple Interest
• - Compound Interest
• Loan Amortization
• Doubling Period
• - Rule 69
• - Rule 72

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Types of Interest

• Simple Interest
• Interest paid or earned on only the
  original amount i.e. the principal amount.
• Compound Interest
• Interest paid or earned on any previous
  interest earned or paid as well as the principal
  amount.

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• Which would you prefer .10,000
• today or .10,000 after 1 year?

Obviously .10,000 today
It means there is Time Value in every
monetary transaction.
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Simple Interest Formula

• FORMULA
• SI Simple Interest
• PV Present Value
• i Rate of Interest
• n Numbers of Years

SIPV (i) (n)
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Compound Interest Formula

• FORMULA
• CI Compound Interest
• P Principal Amount
• i Rate of Interest
• n Numbers of Years

CIP (1i)n
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Difference Between Simple Interest Compound
Interest
P1000 n3yrs. i10

• Simple Interest
• SIPV (i) (n)
• P 1000
• y1 100
• 1100
• y2 100
• 1200
• y3 100
• 1300

• Compound Interest
• CIP (1i)
• P 1000
• y1 100
• 1100
• y2 110
• 1210
• y3 121
• 1331

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F.V .5000 r12 n4yrs.Find P.V

• 1 2 3 4
• 5000 5000 5000 5000

5000 (1.12)
4464.29
5000 (1.12)2
3985.97
5000 (1.12)3
3558.97
5000 (1.12)4
3177.63
15,186.86
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P.V .5000 r12 n4yrs.Find F.V

• 1 2 3 4
• 5000 5000 5000
  5000

5000
5000
5000(1.12)
5600
5000(1.12)2
6272
5000(1.12)2
7024.64
23896.64
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Loan Amortization Schedule

• Most loans are repaid in equal periodic
  installments (monthly, quarterly or annually)
  which cover interest as well as principal
  repayments, such loans are termed as amortized
  loans.

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Example of Loan Amortization Schedule

• A firm borrows .800,000 _at_12 rate of
  interest the loan is to be repaid in 5 equal
  installments payable at the end of each of the
  next 5 years. Prepare loan amortization schedule.
• Solution -
• Present Value of Annuity
• 800,000
  
• 800,000
  
• 800,000
  Amt (3.6059)
• 
  Amt
• 
  221,859

(1r)n -1 r(1r)n
Amt
(10.12)5 -1 0.12(10.12)5
Amt
0.7623 0.2114
Amt
800,0003.6059
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SCHEDULE
Year Opn. Bal. Annual Installment Interest Principal Amt Cl. Bal
(i) (ii) (iii) (ii) -(iii) (iv) (i) -(iv) (v)
1 800,000 221,859 96,000 125,859 674,141
2 674,141 221,859 80,897 140,962 533,179
3 533,179 221,859 63,981 157,878 375,301
4 375,301 221,859 45,036 176,823 198,478
5 198,478 221,859 23,381 198,478 Nil
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Simple Interest Example

• Assume that you deposit .1,000 in an account
  earning 7 simple interest for 2 years. What is
  the accumulated interest at the end of the 2nd
  year?
• SI P (i)(n) 1,000(0.07)(2)
• .140

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Compound Interest Example

• Example Determine the amt available
• in 3 years if 10,000 is deposited now
• at 20 per year?
• Solution-
• F1 10,00010,000(0.20) 12,000
• F2 12,00012,000(0.20) 14,400
• F3 14,40014,400(0.20) 17,280

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Rule of 69

• Rule of 69 0.35
• 
  
• Q. Find doubling period _at_12 rate of interest?
• Solution-
• Rule of 69 0.35
  
• 0.35
  5.75
• 
  6.10years

69 Rate of Interest
69 12
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Doubling Period

• Function
• To know how long it will take to
  double the money at a given rate of interest.
• Method of Doubling Period
• Rule of 72
• Rule of 69.

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Rule of 72
72 Rate of Interest

• Rule of 72
• Q. Find doubling period of 100,000 _at_12 rate of
  interest?
• Solution-
• Rule of 72
• 6years

72 12
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FUTURE VALUE OF AN ANNUITY
Year FVIF _at_ 8 FVIF _at_ 10 FVIF _at_ 12
1 1.0000 1.0000 1.0000
2 2.0800 2.1000 2.1200
3 3.2464 3.3100 3.3744
4 4.5061 4.6410 4.7793
5 5.8666 6.1051 6.3528
Q. 4 equal annual payments of .5000 deposited
in a/c that pays 8 interest p.a. what is Future
Value Of Annuity at the end of 4 yrs? Future
Value Of Annuity .5000 x FVIF _at_ 8
.5000 x 4.5061
.22530.50
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PRESENT VALUE OF AN ANNUITY
Year PVIF _at_ 8 PVIF _at_ 10 PVIF _at_ 12
1 0.9259 0.9091 0.8929
2 1.7833 1.7355 1.6901
3 2.5771 2.4869 2.4018
4 3.3121 3.1700 3.0373
5 3.9927 3.7908 3.6048
Q. What is a Present Value of 4 year Annuity of
.5000 _at_ 10Interest ? PVA
.5000 x
PVIF _at_10
.5000 x 3.1700
.15,850
(1R)n 1 R(1R) n
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