General Maths:Financial Mathematics

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FM4: Credit and Borrowing

Calculation of principal, interest and repayments for flat-rate loans

Flat Rate Loans:

  • Flat or simple interest is charged on the amount borrowed for the term of the loan
  • Examples: banks, credit unions, insurance companies
  • I = Prn
    • P = principal
    • r = rate per period (decimal)
    • n = number of periods


Calculation of values in a table of home loan repayments


Comparison of different options for borrowing money in relation to total repayments, fees, interest rates and flexibility


Calculation of credit-card payments, incorporating fees, charges, rates and interest-free periods

Credit Card Payments:

  • No interest-free period and no annual fee
  • An interest-free period and an annual fee- account is paid in full before the period ends otherwise interest is charged from the date of purchase


Use of published tables from financial institutions to determine monthly repayments on a reducing balance loan

Reducing Balance Loan:

  • Reducible interest
  • Interest is calculated on the balance still owing, not on the principal borrowed


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FM5: Annuities and Loan Repayments

Recognition that an annuity is a form of investment involving periodical, equal contributions to an account, with interest compounding at the conclusion of each period

Annuities:

  • Annuity is a form of investment involving a series of periodic contributions made for a specified time
  • Examples: monthly rent payments, social security benefits, loan repayments
  • Ordinary Annuity- contribution or payment made at the end of each compounding period
  • Ordinary Annuity Due- contribution or payment made at the start of each compounding period


Calculation of the future value (A) of an annuity (or the contribution per period)


Calculation of the present value (N) of an annuity (or the contribution per period)


Using tables to solve problems involving annuities


Use the present value formula for annuities to calculate loan instalments, and hence the total amount paid over the term of a loan


Investigate various processes for repayment of loans


Calculate the fees and charges which apply to different options for borrowing money in order to make a purchase


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FM6: Depreciation

Modelling depreciation by using appropriate graphs, tables and functions using formulae for depreciation:

  • the straight line method
  • the declining balance method


Preparing tables of values and hence developing graphs of against n for different values of r


Comparing the results obtained through each method


Using the above formulae to create and compare depreciation tables


Calculating tax deductions based on depreciation of assets.


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