Bob’s local bank offers 3\% interest per annum on any savings account.
If Bob deposits \$2000, how much will he have after 1 year?
If Bob continues to leave his savings in the account, the interest will be calculated using the new amount we found in part (a). What will the value of his savings be at the end of the second year?
If he repeats the same process for one more year, what will the value of his savings be at the end of the third year?
Is the interest calculated as simple or compound interest?
Determine whether the following statements are true about compound interest:
The interest in any time period is calculated using only the original principal.
Interest is earned on the principal.
Interest is earned on any accumulated interest.
The amount of interest earned in any time period changes from one period to the next.
\$7000 is invested at 6\% p.a. compounded annually. The table below tracks the growth of the principal over 3 years.
Complete the table assuming simple interest is earned each year:
| \text{Time period} \\ (n) | \text{Value at beginning} \\ \text{of time period} | \text{Interest earned at} \\ \text{end of time period} | \text{Amount at end} \\ \text{of time period} |
|---|---|---|---|
| 1 | \$7000 | ||
| 2 | \$420 | ||
| 3 | \$7840 | \$420 |
Complete the following table assuming interest is compounded annually:
| \text{Time period} \\ (n) | \text{Value at beginning} \\ \text{of time period} | \text{Interest earned at} \\ \text{end of time period} | \text{Amount at end} \\ \text{of time period} |
|---|---|---|---|
| 1 | \$7000 | ||
| 2 | \$7865.20 | ||
| 3 | \$7865.20 | \$8337.11 |
Does compound or simple interest lead to greater financial gains?
In which year are the greater financial gains first seen?
\$9000 is invested for 4 years at a rate of 5\% p.a. compounded annually.
Complete the table:
Calculate the total interest accumulated over 4 years.
Calculate the value of the investment at the end of 4 years.
| \text{Interest } (\$) | \text{Balance } (\$) | |
|---|---|---|
| \text{After } 0 \text{ years} | 0 | 9000 |
| \text{After } 1 \text{ year} | ||
| \text{After } 2 \text{ years} | ||
| \text{After } 3 \text{ years} | ||
| \text{After } 4 \text{ years} |
Describe how compound interest is earned.
Calculate the final balance for the following investments, if:
Simple interest was used.
Compound interest was used, compounded annually.
\$1000 is invested for 3 years with an interest rate of 10\% p.a.
\$100\,000 is invested for 5 years with an interest rate of 5\% p.a.
Neil's investment of \$1000 earns interest at 2\% p.a. compounded annually over 2 years. Using the method of repeated multiplication, find the value of the investment after 2 years.
Amber made a single \$20\,000 deposit into a savings account, with interest compounding yearly at 6.8\% p.a. Calculate the balance in the account after 5 years, correct to the nearest dollar.
Buzz's savings of \$4000 earns interest at 4\% p.a. compounded annually over 2 years. Answer the following questions using the method of repeated multiplication:
What is the value of the investment after 2 years?
What is the amount of interest earned?
James’s investment of \$90\,000 earns interest at 5\% p.a. compounded annually over 3 years. Answer the following questions using the method of repeated multiplication:
What is the value of the investment after 3 years?
What is the amount of interest earned?
Use the compound interest formula to find the value of each investment if the interest is compounded annually:
\$1000 at 4\% p.a. for 2 years.
\$550 at 5\% p.a. for 3 years.
\$1400 at 2\% p.a. for 5 years.
\$3000 at 8.5\% p.a. for 8 years.
\$8200 at 3.4\% p.a. for 3 years.
\$12\,250 at 5\dfrac{1}{4}\% p.a. for 10 years.
A \$2870 investment earns interest at 4.4\% p.a. compounded annually over 20 years. Use the compound interest formula to calculate the value of this investment.
Use the compound interest formula to calculate the amount, A, that is owed after 4 years if \$1000 is borrowed at an interest rate of 9\% p.a. compounding annually.
A \$7510 investment earns interest at 4.5\% p.a. compounded annually over 6 years. Use the compound interest formula to calculate the final value of this investment.
Maria’s investment of \$2710 earns interest at 3.3\% p.a. compounded annually over 10 years. How much interest was earned during this period?
\$372 is invested at 5\% p.a. compounded annually for 10 years. After this time, the principal plus interest is reinvested at 6\% p.a. compounded annually for 9 more years.
What is the final value of the investment?
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?
Emma borrows \$7000 from a loan shark at a rate of 4.7\% p.a. compounded annually. She is not able to make any repayments for 3 years. How much does she owe at the end of 3 years?
\$380 is invested at 2\% p.a. compounded annually for 5 years. At the end of 5 years, the entire value of the investment is reinvested at 3\% p.a. compounded annually for 4 more years. What is the final value of the investment at the end of the 9 years?
Kate invests \$3000 at a rate of 2\% p.a. compounded annually. Find how much the investment is worth after:
24 months
18 months
30 months
Ben borrows \$7000 at a rate of 2\% p.a. compounded annually. After 2 years he makes a repayment of \$500. After another 3 years, with no further repayments, how much does Ben owe?
Xavier invests \$7000 in a term deposit with a rate of 2\% p.a. compounded annually. After 3 years he withdraws \$600, and leaves the rest in the the term deposit for 2 more years. How much is the investment worth after the total 5 years?