Interactive practice questions
Rochelle invests $\$190000$$190000 at a rate of $7%$7% per annum compounded annually, and wants to work out how much she can withdraw each year to ensure the investment lasts $20$20 years.
We will use geometric sequences and series to determine what Rochelle's annual withdrawal amount should be if she wants the investment to last $20$20 years.
The amount in the account after $n$n years can be expressed as the $n$nth term of a geometric sequence minus the sum of a different geometric sequence.
Write an expression for the amount in the investment account after $n$n years.
Use $x$x to represent the amount to be withdrawn each year.
Hence determine Rochelle's annual withdrawal amount, correct to the nearest cent.
Gwen received an inheritance of $\$150000$$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.