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Topic 1: Loans, investments and annuities 1

Compound interest loans and investments

6 hours

• Use a recurrence relation to model a compound interest loan or investment. 2 interactives
• +1 = where +1 is total amount at the beginning of the (+ 1) th period, is total amount at the beginning of the th period, and = 1 + where is interest rate per compounding period
• Use the compound interest formula to model a compound interest loan or investment.
• Calculate the effective annual rate of interest, effective, and use the results to compare interest on loans or investments when interest is paid or charged for different compounding periods, including daily, monthly, quarterly and six-monthly. 1 interactive
• effective = (1 +) − 1 where is interest rate per compounding period and is number of compounding periods per year
• Solve practical problems involving compound interest loans or investments, including determining the total amount of the loan or investment, total interest, principal, interest rate per year and per compounding period, and the effect of the interest rate and number of compounding periods on the total amount.

Present value of ordinary annuities

6 hours

• Use a recurrence relation to model the present value of an ordinary annuity, e.g. reducing balance loan or retirement pension with periodic payments where interest is calculated before the periodic payment is made. 1 interactive
• +1 = − where +1 is total amount at the beginning of the (+ 1) th period, is total amount at the beginning of the th period, is periodic payment, and = 1 + where is interest rate per compounding period
• Use the present value annuity formula to model the present value of an ordinary annuity, e.g. reducing balance loan or retirement pension with periodic payments where interest is calculated before the periodic payment is made.
• Solve practical problems involving the present value of an ordinary annuity, including determining the total amount of the annuity, periodic payment, total payments and total interest.