Interactive practice questions
At the start of 2014 Pauline deposits $\$5000$$5000 into an investment account. At the end of each quarter she makes an extra deposit of $\$700$$700. By looking at the pattern investment, Pauline realises she can use her knowledge of geometric series to find the balance in the account at some point in the future.
The table below shows the first few quarters of 2014. All values in the table are in dollars.
| Quarter | Opening Balance | Interest | Deposit | Closing Balance |
|---|---|---|---|---|
| Jan-Mar | $5000$5000 | $200$200 | $700$700 | $5900$5900 |
| Apr-Jun | $5900$5900 | $236.00$236.00 | $700$700 | $6836.00$6836.00 |
| Jul-Sep | $6836.00$6836.00 | $273.44$273.44 | $700$700 | $7809.44$7809.44 |
Use the numbers for the January quarter to calculate the quarterly interest rate.
Write an expression for the amount in the account at the end of the first quarter.
Do not evaluate the expression.
$\editable{}\times\editable{}+\editable{}$×+
Using $5000\times1.04+700$5000×1.04+700 as the starting balance, write an expression for the amount in the account at the end of the second quarter.
$\editable{}\times\left(\editable{}\right)^2+\editable{}\times\editable{}+\editable{}$×()2+×+
Given that the amount in the account at the end of the second quarter can be expressed as $5000\times\left(1.04\right)^2+700\times1.04+700$5000×(1.04)2+700×1.04+700, write a similar expression for the amount in the account at the end of the third quarter.
$\editable{}\times\left(\editable{}\right)^3+\editable{}\times\left(\editable{}\right)^2+\editable{}\times\editable{}+\editable{}$×()3+×()2+×+
The amount in the account after $n$n quarters can be expressed as a term of a geometric sequence plus the sum of a geometric sequence.
Write an expression for the amount in the investment account after $n$n quarters.
Hence determine the total amount in Pauline’s account at the beginning of 2016 to the nearest dollar.
Iain opens an account to help save for a house. He opens the account at the beginning of 2017 with an initial deposit of $\$50000$$50000 that is compounded annually at a rate of $5.9%$5.9% per annum. He makes further deposits of $\$3000$$3000 at the end of each year.
To save up to buy a car, Laura opens a savings account that earns $6%$6% per annum compounded monthly.
She initially deposits $\$1400$$1400 when she opens the account at the beginning of the month, and then deposits $\$165$$165 at the end of every month.
The table below shows the first few years of an investment with regular deposits.