Accounting

1
Accounting Finance for Bankers - Business
Mathematics- Module A

• SPBT College

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Simple Interest
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More Simple Interest
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Compound Interest A FV Perspective
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Compounding
6
Time Line Rs78.35 Invested (5 Years, 5
Interest)
FV5 Rs100
PV Rs78.35
0 1 2
3 4 5
End of Year
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Future Value of Rs200 (4 Years, 8 Interest )
PV Rs200
0 1 2
3 4
End of Year
Compounding the process of earning interest in
each successive year
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FV of a Mixed Cash Flow Stream (5 Years, 5.5
Interest)
FV5 Rs16,689.06
Rs4,335.89
Rs4,462.12
Rs2,226.06
Rs3,165.00
Rs2,500.00
Rs3,500 Rs3,800
Rs2,000 Rs3,000 Rs2,500
0 1 2
3 4 5
End of Year
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Future Value Example
10
Power Of Compound Interest
30.00
20
25.00
15
20.00
Future Value of One Rs)
15.00
10.00
10
5.00
5
0
1.00
0 2 4 6 8 10 12 14 16 18 20
22 24
Periods
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Format of a Future Value Interest Factor (FVIF)
Table
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Computing Future Values Using Excel
You deposit Rs1,000 today at 3 interest. How
much will you have in 5 years?
Excel Function FV (interest, periods, pmt,
PV) FV (.03, 5, ,1000)
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Present Value with Compounding
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Present Value of Rs500(7 Years, 6 Discount
Rate)
0 1 2 3 4
5 6 7
FV7 Rs500
End of Year
PV Rs332.53
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Present Value of Future Amounts (4 Years, 7
Interest )
Discounting
0 1 2
3 4
End of Year
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PV of a Mixed Stream (4 Years, 6 Interest)
0 1 2
3 4
Rs1,500,000 Rs3,000,000
Rs2,000,000 Rs5,000,000
End of Year
Rs1,415,100
Rs2,669,700
Rs1,679,200
Rs3,960,500
PV4 Rs9,724,500
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Present Value Examples
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Format of a Present Value Interest Factor (PVF)
Table
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Calculating PV Of A Single Amount Using Excel
Example How much must you deposit today in order
to have Rs500 in 7 years if you can earn 6
interest on your deposit?
Excel Function PV (interest, periods, pmt,
FV) PV (.06, 7,,500)
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FV PV of Mixed Stream(5 Years, 4 Interest
Rate)
Compounding
- Rs12,166.5
FVRs6,413.8
Rs3,509.6
Rs5,624.3
Rs4,326.4
Rs3,120.0
-Rs10,000 Rs3,000 Rs5,000 Rs4,000
Rs3,000 Rs2,000.0
0 1 2
3 4 5
End of Year
PVRs5,271.7
Rs2,884.6
Rs4,622.8
Rs3,556.0
Rs2,564.4
Rs1,643.9
Discounting
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Annuity Cash Flows
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FV of Ordinary Annuity(End of 5 Years, 5.5
Interest Rate)
Rs1,238.82
Rs1,174.24
Rs1,113.02
Rs1,055.00
Rs1,000.00
Rs1,000 Rs1,000
Rs1,000 Rs1,000 Rs1,000
0 1 2
3 4 5
End of Year
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FV of an Ordinary Annuity Using Excel
How much will your deposits grow to at the end of
five years if you deposit Rs1,000 at the end of
each year at 4.3 interest for 5 years?
Excel Function FV (interest, periods, pmt,
PV) FV (.043, 5,1000 )
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PV of Ordinary Annuity (5 Years, 5.5 Interest)
0 1 2
3 4 5
Rs1,000 Rs1,000 Rs1,000
Rs1,000 Rs1,000
End of Year
Rs947.87
Rs898.45
Rs851.61
Rs807.22
Rs765.13
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Annuity Examples
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Ordinary Annuity vs. An Annuity Due
Annual Cash Flows
End of yeara Annuity A
(ordinary) Annuity B (annuity due)

aThe ends of years 0, 1,2, 3, 4 and 5 are
equivalent to the beginnings of years 1, 2, 3, 4,
5, and 6 respectively
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Calculating the Future Value of an Annuity Due

• Equation for the FV of an ordinary annuity can
  be converted
• into an expression for the future value of
  an annuity due,
• FVAn (annuity due), by merely multiplying by
  (1 r)

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FV of an Annuity Due Using Excel

• How much will your deposits grow to at the end of
  five years
• if you deposit Rs1,000 at the beginning of each
  year at 4.3
• interest for 5 years?

Excel Function FV (interest, periods, pmt,
PV) FV (.043, 5, 1000) Rs5,448.89(1.043)
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Deposits Needed to Accumulate a Future Sum

• A person wishes to buy a house 5 years from
  nowand estimates an initial down payment of
  Rs35,000 will berequired at that time
• She wishes to make equal annual end-of-year
  deposits in an account paying annual interest of
  4 percent, so she must determine what size
  annuity will result in a lump sum equal to
  Rs35,000 at the end of year 5
• Find the annual deposit required to accumulate
  FVAn dollars, given an interest rate, r, and a
  certain number of years, n by solving equation
  PMT

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Loan Amortization Table (10 interest, 4 Year
Term)
Payments
End of year
Beginning-of-year principal(2)
End-of-year principal(2) (4)(5)
Interest.10 x (2)(3)
Loan Payment(1)
Principal(1) (3)(4)
aDue to rounding, a slight difference (Rs.03)
exists between beginning-of-year 4 principal (in
column 2) and the year-4 principal payment (in
column 4)