Title: time value of money
1TIME VALUE OF MONEY
2WHY 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.
3Concept to be clear
- Present Value
- - Simple Interest
- - Compound Interest
- Future Value
- - Simple Interest
- - Compound Interest
- Loan Amortization
- Doubling Period
- - Rule 69
- - Rule 72
4Types 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.
5- 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.
6Simple Interest Formula
- FORMULA
-
- SI Simple Interest
- PV Present Value
- i Rate of Interest
- n Numbers of Years
SIPV (i) (n)
7Compound Interest Formula
- FORMULA
- CI Compound Interest
- P Principal Amount
- i Rate of Interest
- n Numbers of Years
CIP (1i)n
8Difference 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
9F.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
10P.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
11Loan 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.
12Example 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
13SCHEDULE
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
14Simple 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
15Compound 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
16Rule 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
17Doubling 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.
18Rule 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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20FUTURE 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
21PRESENT 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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