Financial Maths
FINANCIAL MATHEMATICS
1. RATE OF RETURN
2. SIMPLE INTEREST
3. COMPOUND INTEREST
4. MULTIPLE CASH FLOWS
5. ANNUITIES
6. LOAN REPAYMENT SCHEDULES
Financial Math Support Materials
Page 1 of 85
(1) RATE OF RETURN
FINANCIAL MATHEMATICS CONCERNS THE
ANALYSIS
OF
CASH
FLOWS
BETWEEN
PARTIES TO A CONTRACT. IF MONEY IS
BORROWED THERE IS AN INTIAL CASH
INFLOW
TO
THE
BORROWER
BUT
AFTERWARDS THERE WILL BE A CASH
OUTFLOW IN THE FORM OF REPAYMENTS.
A person borrows $100 and promises to repay the lender $60 after 1 year and $60 after 2 years.
Show the resulting cash flows for the borrower and lender.
Financial Math Support Materials
Page 2 of 85
Time
Now
1
End of 2 years
Borrower
0
End of 1 year
Lender
2
$100 is loaned out
$120 is received back
The extra $20 is the lenders compensation for foregoing current consumption to obtain future consumption. The lender requires compensation for:
Financial Math Support Materials
Page 3 of 85
THE “TIME VALUE” OF MONEY
CONSIDER A CHOICE OF
$100 NOW, OR
$100 LATER
ANY RATIONAL PERSON WOULD CHOOSE
$100 NOW!
BUT WHY?
“MONEY HAS A TIME VALUE”
Financial Math Support Materials
Page 4 of 85
Time Value of Money (TVM)
Refers to the difference between
The concept enables
Provides the means for valuing multiple cash flows that occur at different times
The level of interest rates is the index used to determine prevailing TVM.
Interest rates are determined by the level of …
For every type of financing transaction there is potentially a different interest rate.
Interest rates are distinguished by the nature of the underlying transaction and focus on three characteristics:
Financial Math Support Materials
Page 5 of 85
An important aspect of valuation is applying the appropriate interest rate.
For example, valuing a fixed-rate loan to a highly speculative company using a
1. RATE OF RETURN
2. SIMPLE INTEREST
3. COMPOUND INTEREST
4. MULTIPLE CASH FLOWS
5. ANNUITIES
6. LOAN REPAYMENT SCHEDULES
Financial Math Support Materials
Page 1 of 85
(1) RATE OF RETURN
FINANCIAL MATHEMATICS CONCERNS THE
ANALYSIS
OF
CASH
FLOWS
BETWEEN
PARTIES TO A CONTRACT. IF MONEY IS
BORROWED THERE IS AN INTIAL CASH
INFLOW
TO
THE
BORROWER
BUT
AFTERWARDS THERE WILL BE A CASH
OUTFLOW IN THE FORM OF REPAYMENTS.
A person borrows $100 and promises to repay the lender $60 after 1 year and $60 after 2 years.
Show the resulting cash flows for the borrower and lender.
Financial Math Support Materials
Page 2 of 85
Time
Now
1
End of 2 years
Borrower
0
End of 1 year
Lender
2
$100 is loaned out
$120 is received back
The extra $20 is the lenders compensation for foregoing current consumption to obtain future consumption. The lender requires compensation for:
Financial Math Support Materials
Page 3 of 85
THE “TIME VALUE” OF MONEY
CONSIDER A CHOICE OF
$100 NOW, OR
$100 LATER
ANY RATIONAL PERSON WOULD CHOOSE
$100 NOW!
BUT WHY?
“MONEY HAS A TIME VALUE”
Financial Math Support Materials
Page 4 of 85
Time Value of Money (TVM)
Refers to the difference between
The concept enables
Provides the means for valuing multiple cash flows that occur at different times
The level of interest rates is the index used to determine prevailing TVM.
Interest rates are determined by the level of …
For every type of financing transaction there is potentially a different interest rate.
Interest rates are distinguished by the nature of the underlying transaction and focus on three characteristics:
Financial Math Support Materials
Page 5 of 85
An important aspect of valuation is applying the appropriate interest rate.
For example, valuing a fixed-rate loan to a highly speculative company using a