# 6.07 Annuities

## Interactive practice questions

Iain invests $\$190000$$190000 at a rate of 7%7% per annum compounded annually. At the end of each year he withdraws \14300$$14300 from the investment after the interest is paid and the balance is reinvested in the account.

We will use the financial solver on our CAS calculator to determine how long the annuity lasts.

a

Fill in the value for each of the following. Type an $X$X next to the variable we wish to solve for.

 $N$N $\editable{}$ $I$I$%$% $\left(\editable{}\right)%$()% $PV$PV $\editable{}$ $PMT$PMT $\editable{}$ $FV$FV $\editable{}$ $P$P$/$/$Y$Y $\editable{}$ $C$C$/$/$Y$Y $\editable{}$
b

At the end of which year will the annuity have run out?

Easy
Approx 4 minutes

Carl invests $\$190000$$190000 at a rate of 12%12% per annum compounded monthly. At the end of each month he withdraws \3900$$3900 from the investment after the interest is paid and the balance is reinvested in the account.

We will use the financial solver on our CAS calculator to determine how long the annuity lasts.

Avril invests $\$190000$$190000 at a rate of 7%7% per annum compounded annually. We will use the financial solver on our CAS calculator to determine what Avril's annual withdrawal should be if she wants the investment to last 2525 years. Victoria invests \190000$$190000 at a rate of $12%$12% per annum compounded monthly.

We will use the financial solver on our CAS calculator to determine what Victoria's equal monthly withdrawal should be if she wants the investment to last $20$20 years.

### Outcomes

#### ACMGM099

use a recurrence relation to model an annuity, and investigate (numerically or graphically) the effect of the amount invested, the interest rate, and the payment amount on the duration of the annuity

#### ACMGM100

with the aid of a financial calculator or computer-based financial software, solve problems involving annuities (including perpetuities as a special case); for example, determining the amount to be invested in an annuity to provide a regular monthly income of a certain amount