\$9000 is invested for three years at a rate of 5\% p.a. compounded annually.
Complete the table:
Calculate the total interest accumulated over 3 years.
Calculate the value of the investment at the end of 3 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} |
\$3000 is invested at 4\% p.a., compounded annually. The table below tracks the growth of the principal over three years.
| \text{Value at start of time period } | \text{Value at end of time period } | \text{Interest earned } | |
|---|---|---|---|
| 1st year | \$3000 | A | B |
| 2nd year | C | \$3244.80 | D |
| 3rd year | \$3244.80 | \$3374.59 | E |
Find the value of:
Find the total interest earned over the three years.
Describe how compound interest is earned.
Use the compound interest formula to calculate the amount, A, that an investment of \$1000 is worth after 3 years at an interest rate of 4\% p.a. compounded annually.
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.
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?
\$4000 is deposited into an account that attracts interest at a rate of 2.5\% per annum. Find the amount of interest accumulated over 8 years if:
Simple interest is used.
The interest is compounded annually.
Amelia borrows \$2400 at a rate of 6.3\% p.a. compounded annually. If she pays off the loan in a lump sum at the end of 5 years, how much interest does she pay?
Sally's investment of \$8910 earns interest at 4\% p.a. compounded annually over 10 years.
How much interest was earned during this period?
Lachlan borrows \$5000 at a rate of 4.5\% compounded annually. After 2 years the bank increases the interest rate to 4.6\%. If he pays off the loan in a lump sum at the end of 5 years, how much interest does he pay?
Bob applies for a loan of \$5000 over 4 years at a rate of 3.5\% per annum. He is offered the choice between simple interest and interest compounded annually.
Over 6 years, an investment accumulated to \$84\,000. If the compound interest rate was 4.6\% p.a. for the entire 6 years, calculate the original amount invested.
Alex borrowed money from the bank for 4 years at a rate of 7.5\% per annum. At the end of the 4 years he owed the bank \$8950. How much did he initially borrow?
Jeremy has just won \$50\,000. When he retires in 15 years, he wants to have \$94\,000 in his fund which earns 6\% interest per annum. How much of his winnings does he need to invest now to achieve this?
Victoria has been promised an inheritance of \$70\,000 in 5 years time. What is the most she can borrow now at a rate of 7\% p.a. compounded annually, and still be able to pay off the loan with her inheritance?