Annuities (DP IB Applications & Interpretation (AI)): Revision Note

Annuities

What is an annuity?

• When a sum of money is owed to you, you can either

  • take it in full (called a lump sum)

  • or have it paid back to you in regular intervals with added interest (an annuity)

• With annuities, you receive more than the original sum of money

• Examples of this situation include

  • money from inheritance

  • money you invest into a growing company

    • with the expectation that they return more than that amount back to you

How do I use the GDC for annuity calculations?

• Your GDC has a finance package

  • for example

    • finance solver mode

    • TVM (time value of money) solver

• Input all the information given in the question into your GDC

  • Leave blank the quantity you are trying to find

  • The GDC will then find this value

• is the number of payment periods

  • e.g. how long you plan to receive regular payments

  • % is the nominal annual interest rate

  • is initial value of the sum of money owed to you

    • or the amount you invest in a company

    • This is entered as a negative number

  • is the payments made per period

    • How much money you receive every period

    • This is a positive number

  • is the future value of the amount owed to you

    • This will be zero if the amount is paid back after the payment periods

  • is the number of payments per year

    • e.g. 12 for monthly payments

  • is the compounding periods per year

    • e.g. 12 for monthly payments

  • is the time during the year (or during the month) at which the payment is made to you

    • assume this is the start of a period, unless told otherwise

What is the formula for annuities?

• There is a formula for annuities, but it is not examinable (it may be useful to enhance understanding):

• Where

  • is the future value

  • is the amount invested

  • is the number of years

  • is the interest rate as a decimal (e.g. at 6%, = 0.06)