4.02 Visualising compound interest
Interactive practice questions
Paul used repeated applications of simple interest to calculate how much an investment of $\$2000$$2000 would grow over $3$3 years if it accrued compound interest at a rate of $22%$22% p.a., compounding annually.
| Balance + interest | Total balance | Interest earned | |
|---|---|---|---|
| Start of investment | $-$− | $\$2000.00$$2000.00 | $\$440.00$$440.00 |
| First year | $\$2000.00+\$440.00$$2000.00+$440.00 | $\$2440.00$$2440.00 | $\$536.80$$536.80 |
| Second year | $\$2440.00+\$536.80$$2440.00+$536.80 | $\$2976.80$$2976.80 | $\$654.90$$654.90 |
| Third year | $\$2976.80+\$654.90$$2976.80+$654.90 | $\$3631.70$$3631.70 | $-$− |
Using the information from the table, which of the following table of values shows the relationship between investment value and the number of years that have passed?
| No. years | $0$0 | $1$1 | $2$2 | $3$3 |
|---|---|---|---|---|
| Investment value ($\$$$) | $2000$2000 | $2440$2440 | $2976.8$2976.8 | $3631.7$3631.7 |
| No. years | $0$0 | $1$1 | $2$2 | $3$3 |
|---|---|---|---|---|
| Investment value ($\$$$) | $440$440 | $536.8$536.8 | $654.9$654.9 | $798.97$798.97 |
| No. years | $1$1 | $2$2 | $3$3 | $4$4 |
|---|---|---|---|---|
| Investment value ($\$$$) | $2000$2000 | $2440$2440 | $2976.8$2976.8 | $3631.7$3631.7 |
| No. years | $1$1 | $2$2 | $3$3 | $4$4 |
|---|---|---|---|---|
| Investment value ($\$$$) | $440$440 | $536.8$536.8 | $654.9$654.9 | $798.97$798.97 |
Which of the following graphs correctly shows the relationship between the number of years passed and the value of the investment?
Is the growth of the investment linear or non-linear?
Linear
Non-linear
Neither
It is too difficult to determine
Amy used repeated applications of simple interest to calculate how much an investment of $\$300$$300 would grow over $3$3 years if it accrued compound interest at a rate of $23%$23% p.a., compounding annually.
Sharon used repeated applications of simple interest to calculate how the value of a boat currently valued at $\$500$$500 would decrease over $3$3 years if it depreciated at a rate of $26%$26% per year.
Which of the following graphs could represent a savings account that earns compound interest over $50$50 years?