IB DP Maths: AI HL复习笔记1.4.2 Amortisation & Annuities

What is amortisation?

• Amortisation is the process of repaying a loan over a fixed period of time
  • Most commonly questions will be about mortgages (loans taken out to buy a home) or loans taken out for a large purchase
• Interest will be paid on the original amount
  • Each repayment that is made will partly repay the original loan and partly pay the interest on the loan
  • As payments are made the amount owed will decrease and so the interest paid will decrease
    • As you continue to repay a loan more of the repayment goes on the loan and less on the interest

How can the GDC be used to make calculations involving loans?

• Your GDC should be used to solve questions involving loans
  • Use the finance solver mode (sometimes called the TVM (time value of money) solver)
    • N will be the number of repayment periods (remember to include months and years if necessary)
    • I (%) is the interest rate
    • PV is the amount that was borrowed at the start – as this has been received it will be entered as a positive number
    • PMT is the payments made per period – this is repaying the loan so will be a negative number
    • FV is the future value (this will be zero as the loan will be paid off at the end of the period)
    • P/Y is the number of payments per year, usually 12 as payments are made monthly
    • C/Y is the compounding periods per year
    • PMT@ is the time of the year or month the payment is made (assume this is the end unless told otherwise)
  • Leave the section that you need to find out blank and fill in all other sections
  • Your GDC will fill in the last part for you
• It is sensible to check your final answer, you can do this by finding the total amount paid back overall and comparing it to the original loan
  • The total amount repaid will be a little more than the original loan plus I % of the original loan

What is an annuity?

• An annuity is a fixed sum of money paid to someone at specified intervals over a fixed period of time
  • Most commonly this will be because of an initial lump sum investment which will be returned at fixed intervals of time with a fixed interest rate
  • Either from personal savings or from receiving an inheritance

How are annuities calculated?

• Your GDC should be used to solve questions involving annuities
  • Use the finance solver mode (sometimes called the TVM (time value of money) solver)
    • N will be the number of payment periods (remember to include months and years if necessary)
    • I (%) is the interest rate
    • PV is the amount that was invested – as this has been invested it will be entered as a negative number
    • PMT is the amount paid per period – as this is being received it will be a positive number
    • FV is the future value (for an annuity this will be zero as the balance at the end of the payment period will be zero)
    • P/Y is the number of payments per year
    • C/Y is the compounding periods per year
    • PMT@ is the time of the year or month the payment is made (usually the start)
  • Leave the section that you need to find out blank and fill in all other sections
  • Your GDC will fill in the last part for you
• Although you are unlikely to need to use it, the formula for calculating an annuity is:

• • Where
    • FV is the future value
    • A is the amount invested
    • n is the number of years
    • r% is the interest rate
  • This formula is not given in the formula booklet, however your GDC will work out annuities for you so you do not need to remember it