Interactive practice questions
Neil and John both inherit $\$12000$$12000 and put their money in compound interest-bearing accounts for a period of $5$5 years.
Neil places his money in an account with an interest rate of $2.75%$2.75% p.a. compounded monthly.
Complete the table of values for Neil’s account showing the value of the investment at the end of each month.
Round your answers to the nearest cent.
| Number of months | $1$1 | $2$2 | $3$3 | $\ldots$… | $60$60 |
|---|---|---|---|---|---|
| Value of investment ($\$$$) | $12027.50$12027.50 | $\editable{}$ | $\editable{}$ | $\ldots$… | $13766.65$13766.65 |
Write a recursive rule for Neil's investment $V_{n+1}$Vn+1 in terms of $V_n$Vn, where $V_n$Vn describes the value of the investment after the $n$nth month, in exact form.
Include the initial investment $V_0$V0, and enter both parts on the same line, separated by a comma.
John places his money in an account which earns interest compounded daily. At the end of the five years, John’s balance is the same as Neil’s balance. Calculate the interest rate per annum for John’s investment account as a percentage.
Round your answer to three decimal places.
Assume there are $365$365 days in a year.
Does the difference in compounding periods mean that John’s interest rate per annum is higher or lower than Neil’s?
Higher
Lower
Roxanne turns $53$53 today and is saving for her planned retirement at $65$65 years of age. She currently has $\$298000$$298000 in her superannuation account. She plans to have $\$750000$$750000 in her account at retirement from which she will receive an annuity each year. The interest rate on her superannuation account is $5.75%$5.75% p.a. compounded monthly, plus she makes a monthly deposit into the account.
Frank wins the lottery and decides to deposit the winnings in a high interest savings account. He has the following two choices.
Elizabeth is given $\$3500$$3500 as a $21$21st birthday present and decides to invest the money in an account where interest is compounded quarterly. She decides to also make a $\$75$$75 per quarter deposit into the account.
The table shows the balance of Elizabeth’s account over the first $5$5 quarters.