16.05 Applications of simple and compound interest
Dave's investment of \$6000 earns interest at 2\% p.a, compounded annually over 3 years.
Using repeated multiplication, find:
The value of the investment after 3 years.
The amount of interest earned.
A \$2090 investment earns interest at 4.2\% p.a. compounded annually over 17 years. Use the compound interest formula to calculate the value of this investment.
Sally's investment of \$8950 earns interest at 4\% p.a. compounded annually over 4 years. Find the amount of interest earned.
\$3900 is invested for three years at a rate of 10\% p.a., compounding annually.
Complete the table below to determine the final value of the investment:
| Balance + interest | Total balance | Interest earned | |
|---|---|---|---|
| First year | - | \$3900 | \$390 |
| Second year | \$3900 + \$390 | \$4290 | \$429 |
| Third year | |||
| Fourth year | - |
Calculate the total interest earned over the three years.
State whether the following is true about compound interest:
Interest is earned on the principal.
The interest in any time period is calculated using only the original principal.
Interest is earned on any accumulated interest.
The amount of interest earned in any time period changes from one period to the next.
What is the value of a \$1330 brand new desk after 7 years when the annual inflation rate is 11\%?
In 2001, the price of a bottle of orange juice was \$3.20. What was the price of a bottle of orange juice in 2006 if the inflation rate was 8\% p.a.?
For an inflation rate of 7.4\% per year, what is the expected value of a \$210 basket of groceries 7 years from now?
A one year sports club membership currently costs \$332. Calculate the cost in 6 years time if the inflation rate is 2.6\% per annum. Round your answer to the nearest dollar.
In terms of today's dollar, what will be the value of \$5 in 15 years time if the inflation rate is:
2.1\%
4.1\%
Find the original price of the following items:
A hat today costs \$35.50. Find the price of the hat 9 years ago at an inflation rate of 3.7\% per annum.
An item costs \$15\,000 today. Find the price of the item 4 years ago at an inflation rate of 3.5\% per annum.
The price of pens and pencils in 1996 was \$5. If the value inflated at an average rate of 3.2\% per annum, what would the price have been in 2005?
What is the value of a wine collection, currently valued at \$4790, after 10 years if its rate of appreciation is 9\% p.a.?
The value of land is expected to grow by 6.8\% each year for the next 5 years. If it currently costs \$460 per square metre, how much will it cost at the end of 5 years?
Due to dwindling supplies of oil, oil prices are expected to appreciate by 7.2\% p.a. If the current price of oil is \$79 a barrel, what is the expected price of a barrel in 23 years time?
A house was valued 6 years ago to be worth \$548\,000. Its value appreciated at 5.2\% p.a. What is its appreciated value? Give your answer to the nearest dollar.
If a piece of land appreciates at an average rate of 3.7\% per annum and its current value is \$430\,000, calculate its value in 3 years. Give your answer to the nearest dollar.
A high interest bank account deposit appreciates at 6.6\% per annum and is currently valued at \$46\,000. What will its value be in 8 years? Give your answer to the nearest dollar.
Sean deposits \$4000 into a new savings account. The amount increased by 3.3\% each year for 4 years. Find the new value of the deposit after appreciation, giving your answer to the nearest dollar.
The federal government wants to increase funding to a certain program over 8 years at a constant rate of 4.75\% per annum over that time period. If the initial funding was \$14\,000\,000, find the value of the funding (to the nearest dollar) after:
1 year
4 years
8 years
A vintage collectors item that costs \$6000, appreciates at approximately 6.6\% p.a. After how many full years, n, will the value of the vintage collectors item be over \$15\,000?
There were 10\,100 digital sales of a particular song in its first month of release. The number of monthly digital sales decreased by 360 each month after.
The song registered 7580 digital sales in a particular month. What was the decrease in the monthly sales from the first month?
In how many months after the initial month of release did the song register 7580 in monthly digital sales?
Production robots to be used in a car manufacturing plant were purchased for \$4\,455\,000. After 5 years, they depreciated to a value of \$4\,385\,000.
What was the annual depreciation using the straight-line method?
After 7 years, the robots are sold off. If they continue to depreciate at an annual rate of \$14\,000, how much can they be sold for?
The following graph shows the depreciation of a car's value over 4 years:
What is the initial value of the car?
By how much did the car depreciate each year?
After how many years will the car be worth \$14\,400?
What is the value of the car after 4 years?
Marge purchased shares at a total value of \$99\,800. After 6 months, the shares had dropped in value to \$99\,200.
What is the monthly depreciation using the straight-line method?
Sketch the graph showing the depreciation of the value of the shares over 6 years.
What is the gradient of the line?
What does the gradient represent in context?
What is the value of the y-intercept of the line?
What does the y-intercept represent in context?
Let V represent the value of the shares after n months. Write the equation of the line.
Find the value of the shares after 5\dfrac{1}{2} years.