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.  𝐴𝑃𝑉 = 𝑑 (1−(1+𝑖)−𝑛 𝑖) where 𝐴𝑃𝑉 is total amount, 𝑑 is periodic payment, 𝑖 is interest rate per compounding period and 𝑛 is number of compounding periods

Maree plans to retire at age 65 and wants to arrange a monthly pension that will provide her with regular income. She approaches a financial adviser who offers her a pension plan modelled on an ordinary annuity, where interest is calculated on the balance before each monthly payment is withdrawn. The details of three pension options are shown in the table below. **a)** Use the present value annuity formula to determine the lump sum (present value) Maree must invest in Option B to receive monthly payments of \(\$2{,}400\) for 20 years at \(5.4\%\) per annum, compounded monthly. Give your answer to the nearest dollar. **(3 marks)** **b)** Calculate the total amount Maree will receive over the 20-year period under Option B. **(1 mark)**

A retirement annuity will pay the retiree $\$3{,}500$ at the end of every quarter for the next 15 years. The fund earns interest at $5.2\%$ per annum, compounded quarterly. Use the present value annuity formula to calculate the present value of this annuity, correct to the nearest dollar.

Determine the monthly repayment on a reducing balance loan of $420,000 at 5.4% per annum, compounded monthly, over 30 years. Give your answer to the nearest dollar.