Duke University NROTC 04 March 2014 Personal Financial Management.
Personal Financial Management
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Transcript of Personal Financial Management
Personal Financial Management
Semester 2 2008 – 2009
Gareth Myles [email protected]
Paul Collier [email protected]
Interest and Interest Rates
Some basic information on interest rates Bank of England base rate
Set by Monetary Policy Committee Provides a basis for other rates No-one can trade at a lower rate (arbitrage)
Objectives of the MPC To control the rate of inflation (target band)
Increase in interest rate reduces demand Reduction in interest rate stimulates demand
Base decisions on economic data
Other Important Rates
LIBOR: London Interbank Offered Rate The rate at which banks are willing to lend to each
other The basis for many financial calculations
Mortgage rates Mortgages are the safest form of lending to
individual so have lowest interest rates Market rate is determined by competition between
lenders
Other Important Rates
Personal loans Loans for purchases other than property (more risk) Higher interest rate than mortgages More variation in interest rates than for mortgages
Collateral Secured loan: an asset is held as collateral Unsecured loan: no collateral Interest rate is lower on a secured loan
Credit Creation
How does the banking system function? Savers deposits funds At any time only a fraction of funds withdrawn The remaining fraction leant to borrowers The process is repeated eventually multiplying
initial deposit Banks profit from the difference in interest rates So borrowing rate is higher than the saving rate
(lack of competition, asymmetric information, risk)
Loans
Open-ended An upper limit is agreed, borrower has flexibility
Specific For the purchase of a defined item, with a clear
payment schedule What determines the interest rate?
Lowest when secured on a safe asset Highest when unsecured and open Depends also on credit worthiness of borrower
Profit
Earning money from issuing loans is easy Lenders borrow at one rate Lend at a higher rate
A loss can occur through default and poor risk management Current bank losses can be interpreted as poor risk
management Bad debts increase costs This is why those perceived to be safe will be
offered a lower rate of interest
Credit Rating Agencies
Hold data on borrowers to advise lenders of previous history
Can make mistakes For example assigning bad risk to an address
If refused credit Can ask whether because of a credit agency report Can then contact agency to correct any false
information
Credit Cards
Credit Cards: offer free credit if repaid monthly, but otherwise incur a very high interest rate Table of Rates Strategy: carry debt from card to card to take
advantage of introductory offers
Store Cards: usually an even higher rate Store Card The only reason to hold these is to benefit from
card-holder discounts
Interest Rate Calculations
To understand interest rates, need to go some through some basic calculations
Interest is compounded at a specified intervalThe interval can make a difference
Assume interval is one year Then borrowing £100 at a rate of 10% for one year
implies a total repayment of
110£1.1100£1100£ r
Compounding Interval
Now consider what happens if we compound interest more frequently If every 6 months, then rate of 10% for a year
becomes 5% for six months so
If compounded every 3 months
The general formula for interest at rate r compounded m times a year for n years on a loan of L is
25.11005.110011100 2 rr
38.110025.11001111100 4 rrrr
mn
mr
L
1
Continuous Interest Continuous interest is the limit of more
frequent compounding: Frequency Repayment Cost of £100 at
10%
Annually (m = 1) 110
Semi-annually (m = 2) 110.25
Quarterly (m = 4) 110.38
Monthly (m = 12) 110.47
Weekly (m = 52) 110.51
Daily (m = 365) 110.52
Continuous (m = ) 110.52
rTe100
Effects
The difference between £110 and £110.52 may seem small It is equivalent to 0.52% on the annually-
compounded interest rate of 10% On a large loan this could be significant effect Compounding period
Matters for repayment Needs to be clarified before alternative loans can
be compared
Flat Rate Interest
Interest can also be quoted as a flat rate Consider £100 borrowed for 5 years, with a flat
rate of interest of 10% This means £10 of interest is paid per year
Over 5 years the total payments on the loan are
£10+£10+£10+£10+£10+£100 = £150 The repayment structure is 5 payments of £30 This is equivalent to an APR of 15.2% (see
later or use mortgage calculation)
Annual Percentage Rate
These compounding issues motivate the need to find a standard of comparison
The government has chosen to use the Annual Percentage Rate (APR)
This interest rate converts any interest schedule (such as the flat rate) to the annual equivalent Annual Percentage Rate
Annual Percentage Rate
Consider receiving m payments Ak at times tk and making n payments Ak′ at times tk ′
The interest rate that makes the present discounted value of both flows equal solves
The solution r to this equation is the APR
n
kt
km
kt
k
kk r
A
r
A
1''
1 1
'
1
Example 1
Receive £100 at t1 = 0
Pay £10 at t1′ = 1, pay £110 at t2′ = 2
Solution is r = 10% This is just a standard loan at 10% interest
210 1
110
1
10
1
100
rrr
Example 2
Receive £100 at t1 = 0, receive £50 at t2 = 1.5
Pay £90 at t1′ = 1, pay £80 at t2′ = 2
Solution is r = 13.5% How is this found?
Draw a graph Trial and error
215.10 1
80
1
90
1
50
1
100
rrrr
Example 2
-20
-15
-10
-5
0
5
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2r
215.10 1
80
1
90
1
50
1
100
rrrr
Example 3
Flat rate interest of 10% £100 is received at time 0 Five payments of £30 are made The APR solves
The solution is 15.2% as claimed earlier
543210 1
30
1
30
1
30
1
30
1
30
1
100
rrrrrr
Example 3
-50
-40
-30
-20
-10
0
10
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2r
543210 1
30
1
30
1
30
1
30
1
30
1
100
rrrrrr