Personal Financial Management Semester – 2009 Gareth Myles Paul Collier

Reading Callaghan: Chapter 4 McRae: Chapter 8

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 Savers deposits funds At any time only a fraction of funds withdrawn The remaining fraction leant to borrowers The process is repeated eventually multiplying initial deposit Banks profit from the difference in interest rates So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 interval The 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

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

Continuous Interest Continuous interest is the limit of more frequent compounding: FrequencyRepayment Cost of £100 at 10% Annually ( m = 1) 110 Semi-annually (m = 2) Quarterly (m = 4) Monthly (m = 12) Weekly (m = 52) Daily (m = 365) Continuous (m = )

Effects The difference between £110 and £ 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

Consider receiving m payments A k at times t k and making n payments A k ′ at times t k ′ The interest rate that makes the present discounted value of both flows equal solves The solution r to this equation is the APR

Example 1 Receive £100 at t 1 = 0 Pay £10 at t 1 ′ = 1, pay £110 at t 2 ′ = 2 Solution is r = 10% This is just a standard loan at 10% interest

Example 2 Receive £100 at t 1 = 0, receive £50 at t 2 = 1.5 Pay £90 at t 1 ′ = 1, pay £80 at t 2 ′ = 2 Solution is r = 13.5% How is this found? Draw a graph Trial and error

Example 2

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

Example 3

Comparison The APR is quoted with all adverts for loans It is a simple means of contrasting the rates on loans with different structures