State whether the following are 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.
\$4000 is invested at 2\% p.a. compounded annually. The table below tracks the growth of the principal over three years:
| \text{Time Period }\\ n\text{ (years)} | \text{Value at beginning}\\ \text{ of time period} | \text{Value at end}\\ \text{ of time period} | \text{Interest earned}\\ \text{in time period} |
|---|---|---|---|
| 1 | \$4000 | ||
| 2 | \$4161.60 | ||
| 3 | \$4161.60 | \$4244.83 |
Complete the table.
Find the total interest earned over the three years.
\$3900 is invested for three years at a rate of 10\% p.a. compounded annually.
Complete the table below to determine the final value of the investment:
| Balance at beginning of year | Interest earned | |
|---|---|---|
| First year | \$3900 | \$390 |
| Second year | \$4290 | \$429 |
| Third year | ||
| Fourth year | - |
Calculate the total interest earned over the three years.
\$3700 is invested for three years at a rate of 7\% p.a. compounded annually.
Complete the table below to determine the final value of the investment:
| Balance at beginning of year | Interest earned | |
|---|---|---|
| First year | \$3700 | \$259 |
| Second year | \$3959 | \$277.13 |
| Third year | ||
| Fourth year | - |
Calculate the total interest earned over the three years.
\$520 is invested for two years at a rate of 9\% p.a. compounding annually.
Complete the table below to determine the final value of the investment:
| Balance at beginning of year | Interest earned | |
|---|---|---|
| First year | \$520 | |
| Second year | \$51.01 | |
| Third year | - |
Calculate the total interest earned over the two years.
\$6100 is invested for two years at a rate of 8\% p.a. compounding annually.
Complete the table below to determine the final value of the investment:
| Balance at beginning of year | Interest earned | |
|---|---|---|
| First year | \$6100 | |
| Second year | \$527.04 | |
| Third year | - |
Calculate the total interest earned over the two years.
Maria invested \$1400 at 10\% p.a. compounded annually over 3 years. Without using the compound interest formula, calculate:
The interest earned for the first year.
The balance after the first year.
The interest earned for the second year.
The balance after the second year.
The interest earned for the third year.
The balance after the third year.
The total amount of interest earned over the three years.
The interest as a percentage of the initial investment, correct to one decimal place.
The interest earned after three years if the investment was simple interest rather than compound interest.
Which type of interest is best for this investment and by how much is it better.
Ned's investment of \$90\,000 earns interest at 6\% p.a. compounded annually over 5 years.
Find the value of the investment after 5 years.
Find the amount of interest earned.
Dave's investment of \$6000 earns interest at 2\% p.a. compounded annually over 3 years.
Find the value of the investment after 3 years.
Find the amount of interest earned.
Sharon borrows \$20\,000 at a rate of 4.9\% p.a. compounding annually.
After 3 years, Sharon repays the loan all at once. How much money does she pay back in total?
Find the amount of interest earned on the loan.
Calculate the amount that an investment of \$1000 is worth after 3 years at an interest rate of 4\% p.a. compounded annually.
Calculate the amount that is owed after 4 years if \$1000 is borrowed at an interest rate of 9\% p.a. compounding annually.
Joan's investment of \$3000 earns interest at a rate of 3\% p.a, compounded annually over 4 years. What is the value of the investment at the end of the 4 years?
John borrows \$6000 from a loan shark at a rate of 20\% p.a. compounded annually. He is not able to make any repayments for 5 years. How much does he owe at the end of 5 years?
The spreadsheet below shows the first year of an investment:
| A | B | C | D | |
|---|---|---|---|---|
| 1 | \text{Year} | \text{Beginning Balance} | \text{Interest} | \text{End Balance} |
| 2 | 1 | 8000 | 500 | 8500 |
| 3 | 2 | |||
| 4 | 3 | |||
| 5 | 4 |
Calculate the annual interest rate for this investment.
Write a formula for cell \text{B}3 in terms of one or more other cells.
Write a formula for cell \text{C}3 if the account earns:
Simple interest.
Compound interest, compounded annually.
Write a formula for cell \text{D}3 in terms of one or more other cells.
Using a spreadsheet program, reproduce this spreadsheet and determine the end balance for the 4th year if the account earns:
Simple interest.
Compound interest, compounded annually.
How much more interest is earned over 4 years if the account earns compound interest compared to simple inerest?
The spreadsheet below shows the first year of an investment:
| A | B | C | D | |
|---|---|---|---|---|
| 1 | \text{Initial Investment} | 20\,000 | ||
| 2 | \text{Annual Interest Rate} | 0.072 | ||
| 3 | ||||
| 4 | ||||
| 5 | \text{Year} | \text{Beginning Balance} | \text{Interest} | \text{End Balance} |
| 6 | 1 | 20\,000 | 1440 | 21\,440 |
| 7 | 2 |
Write a formula for cell \text{B}7 in terms of one or more other cells.
Write a formula for cell \text{C}7 if the account earns:
Simple interest.
Compound interest, compounded annually.
Write a formula for cell \text{D}7 in terms of one or more other cells.
Using a spreadsheet program, reproduce this spreadsheet and determine the balance at the end of 5 years if the account earns:
Simple interest.
Compound interest, compounded annually.
How much more interest is earned over 5 years if the account earns compound interest compared to simple inerest?
The following spreadsheet shows the balance in a savings account over 6 years, where interest is compounded yearly:
| A | B | C | D | |
|---|---|---|---|---|
| 1 | \text{Year} | \text{Balance at the beginning} \\ \text{of year} | \text{Interest} | \text{Balance at the end} \\ \text{of year} |
| 2 | \text{1} | \$3000 | \$30 | |
| 3 | \text{2} | \$3030 | \$30.30 | \$3060.30 |
| 4 | \text{3} | \$3060.30 | \$3090.90 | |
| 5 | \text{4} | \$30.91 | \$3121.81 | |
| 6 | \text{5} | \$3121.21 | \$31.22 | \$3153.03 |
Use a spreadsheet to complete the table.