#FinancialMathematics #Year12 #Advanced >[!info]- [Financial mathematics | NSW Curriculum Website](https://curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-advanced-11-12-2024/content/n12/fa4572a048) >- MAV-12-08 models and solves problems to make informed decisions about financial situations ## 📖 Prior Knowledge | Content | Prior knowledge | Used for | | ----------------------------------------- | ------------------------------- | ---------------------------- | | [[Financial Mathematics B]] | - compound interest | - *repeated content* | | [[Exponential and Logarithmic Functions]] | - solving exponential equations | - compound interest problems | | [[Sequences and Series]] | - geometric sequence | - annuities | ## Reducing balance loans - Recognise a reducing balance loan algebraically as a compound interest loan with periodic repayments - Examine the effect of varying the interest rate and repayment amount on the time taken to repay a loan, with or without digital tools or by using a given graph - Solve problems that involve reducing balance loans by calculating the total amount paid, equal periodic repayments, the amount still owing and the time taken to repay the loan ## Annuities - Identify an annuity as either an investment account with regular, equal contributions and interest compounding at the end of each period, or as a single sum investment from which regular equal withdrawals are made - Define and model the future value of an annuity as the sum of all the payments, together with the interest they have earned - Examine the effect of varying the amount initially invested, the value of the periodic payment, the interest rate and the duration of the annuity on the total value of the investment, using digital tools - Solve problems involving annuities in which payments are made at the end of each time period and the future value of an annuity is calculated at the end of one of these periods using the formula for the sum of the first $n$ terms of $a$ geometric sequence