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6.06 Analysing investments with periodic withdrawals

Interactive practice questions

Aaron has saved $\$750000$$750000 for his retirement and sets up an annuity fund on January $1$1st which pays $3.5%$3.5% p.a compounded quarterly. He makes a $\$9000$$9000 per month withdrawal.

a

Determine the number of whole months that he will be able to withdraw from this annuity.

b

If Aaron wishes his annuity to last for $10$10 years, what monthly withdrawal should he make?

Round your answer to the nearest cent.

Medium
1min

Lachlan received an inheritance of $\$100000$$100000. He invests the money at $8%$8% per annum with interest compounded annually at the end of the year. After the interest is paid, Lachlan withdraws $\$9000$$9000 and the amount remaining in the account is invested for another year.

Medium
5min

Christa wins a prize of $\$80000$$80000. She invests the money at $12%$12% per annum with interest compounded monthly at the end of each month. At the start of each month, before interest is earned, Christa withdraws $\$1100$$1100 and the amount remaining in the account is invested.

Medium
4min

Gwen received an inheritance of $\$150000$$150000. She invests the money at $6%$6% per annum with interest compounded annually at the end of the year. After the interest is paid, Gwen withdraws $\$10000$$10000 and the amount remaining in the account is invested for another year.

Medium
5min
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Outcomes

4.1.3.1

use a recurrence relation A_(n+1)=𝑟A_𝑛+𝑑 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

4.1.3.2

solve problems involving annuities, including perpetuities as a special case, e.g. determining the amount to be invested in an annuity to provide a regular monthly income of a certain amount

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