FSMQ Level 3 (pilot) Mathematical principles for personal finance scheme of work
Before starting this Advanced (Level 3) FSMQ, students should have acquired the skills and knowledge associated with the Number and Algebra assessment objective of GCSE Mathematics, or with an Intermediate (Level 2) FSMQ Finance course, or equivalent.
A suggested work scheme showing topics and methods to be covered is given below. The order in which the topics are covered and the time allocated to them can be varied to suit different groups of students.
Topic area 
Content 
Nuffield resources 
Percentages and personal taxation 
Calculate % change = x 100 Use multipliers to combine % changes (including repeated changes) and to reverse % changes  including VAT. Carry out complex calculations involving multiple rates – including income tax, national insurance, capital gains tax. 
Working with percentages 
Income Tax 

National Insurance 

Saving 
Class discussion  Would it be better to receive a sum of money (such as £5000) now or at a later date (such as 20 years from now)? Discuss the key idea of present value (PV) and future value (FV). Collect and discuss information about interest rates from banks, building societies and other sources. (Include information given in the form of tables and diagrams.) Use ideas of compound interest to introduce the formula FV = PV(1 + r)^{n} where r is the interest rate expressed as a decimal and n is the number of time periods. Apply recurrence relations such as . Also transform to and apply this to find present values. Include the use of both a calculator and spreadsheet (if possible). AER: Calculate the annual effective interest rate, , given a nominal interest rate, where is the number of compounding periods per year.

Savings growth 
Topic area 
Content 
Nuffield resources 
Indices 
Use data relevant to students' other studies or interests to introduce the idea of an index as a ratio that describes the relative change in a variable (e.g. price) compared to a certain base period (such as one year). Include examples from the National Statistics website at www.statistics.gov.uk (such as indices for prices, earnings, building costs, manufacturing output, motor vehicle production, and retail sales volumes). Include % change = for areas of finance such as the FTSE 100 share index. Research and compare the Retail Price Index (RPI) and Consumer Price Index (CPI). Include calculation from the Laspeyres Index formula (weighted by quantities in the base period): x 100 where P_{it} is the price of commodity at time t, and Q_{it} is the quantity of commodity at time t. 0 represents the base period, so for example Q_{i0} represents the quantity of commodity i at the base period ( t = 0 ) 
Average earnings index 
Inflation indices 

Laspeyres Index 

Data over time 
Inspect tables and graphs considering changes over time. Include data over different time intervals (such as daily, weekly, quarterly). Interpret trends (such as in stocks & shares, interest rates, exchange rates). Represent data graphically and find linear equations to model data using gradient and intercept and algebraic substitution. Calculate average changes. Use moving averages to smooth shortterm fluctuations and interpret situations (eg involving indices such as the 100 share index). Include seasonal and cyclical variations.
Moving averages:
Calculate successive values using
Address the problem of lag using weighting and calculate the linear weighted moving average where the denominator is the triangular number with sum . Understand that this can be considered to lag behind the trend. 
House prices moving averages 
Topic area 
Content 
Nuffield resources 
Borrowing 
APR (annual percentage rate) 
APR – Annual Percentage Rate 
Financial diagrams 
Make sense of a range of information presented in tables and diagrams relating to finance. Include tabulated information about savings, loans, credit card accounts, shares, ISAs (etc.) and information in the form of graphs and charts. 
Financial graphs and charts 
Weighted averages 
Calculate contributions made by individual items to indices. For instance calculate contributions made by the prices of commodities in different shops and regions to a consumer price index. For example, if a commodity costs £5 in shop A and £6 in shop B and 40% (0.4) of customers buy the commodity from shop A and 60% (0.6) from shop B, the effective cost of the commodity used in calculating an index is 0.4 × £5 + 0.6 × £6 = £5.60 Calculate a composite index by combining indices using weighting (for instance in calculating a price index the index of each commodity multiplied by its weighting is totalled, and this sum is divided by the sum of all the commodities weights). 

Further borrowing 
Use more complex recurrence relations such as for credit cards, mortgages. Find APR (annual percentage rate) for a loan repaid in a small number of instalments (such as 2, 3 or 4). using loan:
· substituting values into the above equation for confirmation, · solving the above equation for i using the interval bisection method. Include applications to financial areas such as loans, credit cards, mortgages. 
Credit cards 
APR with more than one instalment 
Topic area 
Content 
Nuffield resources 
Further indices 
Use the Paasche index formula (weighted by quantities in the calculation period):
where P_{it} is the price of commodity at time t,
Compare Laspeyres, Paasche and Fischer indices. 

More tables and diagrams 
Use information given in more complex tables relating to personal finance. Discuss and make sense of a range of less familiar charts eg hilow charts, candlestick charts, Kagi charts. 
Financial charts and graphs 
Continuous compounding 
Introduce and use the idea that continuous compounding leads to exponential functions. That is:
is the amount after t years for an initial investment of _{ }when the interest is compounded n times per year, and 

Revision 
Revise topics. Work through revision questions and practice papers. Discuss the data sheet  make up and work through questions based on it. 
Financial calculations 
Page last updated on 25 January 2012