4.02 Visualising compound interest
State whether the following graphs could represent a savings account that earns compound interest over 50 years:
Consider the following graph showing two investments, one with simple interest (Investment A) and another with compound interest (Investment B):
Which investment has a higher principal amount?
Which investment has a higher final amount after 10 years?
After how many years will the investments be equal in value?
\$1000 is invested for 10 years with an interest rate of 10\% per annum that includes the accumulated interest.
Is this an example of simple or compound interest? Explain your answer.
Sketch a graph showing the growth of the investment.
Paul used repeated applications of simple interest to calculate how much an investment of \$2000 would grow over 3 years if it earned compound interest at a rate of 22\% p.a., compounded annually:
| Year | Balance + interest | Value | Interest earned |
|---|---|---|---|
| \text{Start of investment, } 0 | \qquad \quad \enspace - | \quad \quad \$ 2000.00 | \qquad \$440 |
| \text{First year, } 1 | \quad \$ 2000.00 + \$440.00 | \qquad \$ 2440.00 | \qquad \$ 536.80 |
| \text{Second year, } 2 | \quad \$ 2440.00 \, + \$ 536.80 | \qquad \$ 2976.80 | \qquad \$654.90 |
| \text{Third year, }3 | \quad \$ 2976.80 + \$654.90 | \qquad \$ 3631.70 | \qquad\quad - |
Plot the relationship between the number of years passed and the value of the investment.
Is the growth of the investment linear or non-linear?
Amy used repeated applications of simple interest to calculate how much an investment of \$300 would grow over 3 years if it earned compound interest at a rate of 23\% p.a., compounded annually:
| Year | Balance + interest | Value | Interest earned |
|---|---|---|---|
| \text{Start of investment, }0 | \qquad \quad \enspace - | \quad \quad \$ 300.00 | \qquad \$69.00 |
| \text{First year, }1 | \quad \$ 300.00 + \$ 69.00 | \qquad \$ 369.00 | \qquad \$ 84.87 |
| \text{Second year, }2 | \quad \$ 369.00 \, + \$ 84.87 | \qquad \$ 453.87 | \qquad \$104.39 |
| \text{Third year, }3 | \quad \$ 453.87 + \$104.39 | \qquad \$ 558.26 | \qquad\quad - |
Plot the relationship between the number of years passed and the value of the investment.
Is the growth of the investment linear or non-linear?
William used repeated applications of simple interest to calculate how much an investment of \$400 would grow over 3 years if it earned interest at a flat rate of 6\% p.a., compounded annually:
| Year | Balance + interest | Value | Interest earned |
|---|---|---|---|
| \text{Start of investment, }0 | \qquad \quad \enspace - | \quad \quad \$ 400.00 | \qquad \$24.00 |
| \text{First year, }1 | \quad \$ 400.00 + \$ 24.00 | \qquad \$ 424.00 | \qquad \$ 24.00 |
| \text{Second year, }2 | \quad \$ 424.00 \, + \$ 24.00 | \qquad \$ 448.00 | \qquad \$24.00 |
| \text{Third year, }3 | \quad \$ 448.00 + \$24.00 | \qquad \$ 472.00 | \qquad\quad - |
Plot the relationship between the number of years passed and the value of the investment.
Is the growth of the investment linear or non-linear?
Sharon used repeated applications of simple interest to calculate how the value of a boat currently valued at \$500 would decrease over 3 years if it depreciated at a rate of 26\% per year:
| Year | Balance + interest | Value | Depreciation |
|---|---|---|---|
| \text{Current value, }0 | \qquad \quad \enspace - | \quad \quad \$ 500.00 | \qquad \$130.00 |
| \text{First year, }1 | \quad \$ 500.00 - \$ 130.00 | \qquad \$ 370.00 | \qquad \$ 96.20 |
| \text{Second year, }2 | \quad \$ 370.00 \, - \$ 96.20 | \qquad \$ 273.80 | \qquad \$71.19 |
| \text{Third year} | \quad \$ 273.80 - \$71.19 | \qquad \$ 202.61 | \qquad\quad - |
Plot the relationship between the number of years passed and the value of the boat.
Is the depreciation of the boat's value linear or non-linear?
Luke invests \$50 into an account which accumulates interest at a rate of 8\% p.a., compounded annually.
Plot the relationship between the number of years passed and Luke's account balance.
How many years will it take for the account to reach a total value of \$200?
Skye invests \$700 into an account which accumulates interest at a rate of 9\% p.a., compounded annually.
Plot the relationship between the number of years passed and Skye's account balance.
How many years will it take for the account to reach a total value of \$2800?
The value of a coin valued at \$900 appreciates in value at a rate of 8\% per year.
Plot the relationship between the number of years passed and the coin's value.
How many years will it take for the coin's value to reach a total value of \$2300?
The value of a plane valued at \$6500 depreciates in value at a rate of 22\% per year.
Plot the relationship between the number of years passed and the plane's value.
How many years will it take for the plane's value to reach a value of \$1100?
Pauline invests \$600 into a fund which accumulates interest at a rate of 8\% p.a., compounded annually.
Plot the relationship between the number of years passed and the value of Pauline's fund.
Find the value of the fund be after seven years. Round your answer to the nearest 100dollars.
Jimmy invests \$2000 into a fund which accumulates interest at a rate of 6\% p.a., compounded annually.
Plot the relationship between the number of years passed and the value of Jimmy's fund.
Find the value of the fund be after five years. Round your answer to the nearest 100 dollars.
Vincent owns a tank currently valued at \$4500 which depreciates at a rate of 28\% per year.
Plot the relationship between the number of years passed and the value of Vincent's tank.
Find the value of the tank after seven years. Round your answer to the nearest 100 dollars.