Describe how compound interest is earned.
\$9000 is invested for 3 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.
A \$7510 investment earns interest at 4.5\% p.a. compounded annually over 6 years.
For the compound interest formula A=P(1+i)^n, state the value of:
Calculate the value of A.
A \$3400 investment earns interest at 3\% p.a. compounded quarterly over 19 years.
For the compound interest formula A=P(1+i)^n, find the value of:
Calculate the value of A.
A \$9090 investment earns interest at 4.7\% p.a. compounded semiannually over 11 years.
For the compound interest formula A=P(1+i)^n, find the value of:
Calculate the value of A.
A \$8920 investment earns interest at 3.3\% p.a. compounded monthly over 5 years.
For the compound interest formula A=P(1+i)^n, find the value of:
Calculate the value of A.
A \$3420 investment earns interest at 2.6\% p.a. compounded weekly over 9 years. Assume there are 52 weeks in one year.
For the compound interest formula A=P(1+i)^n, find the value of:
Calculate the value of A.
A \$6000 investment earns interest at 7.3\% p.a. compounded daily over 11 years. Assume there are 365 days in one year.
For the compound interest formula A=P(1+i)^n, find the value of:
Calculate the value of A.
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?
Calculate the amount, A, that an investment of \$1000 compounded annually is worth after:
3 years at an interest rate of 4\% p.a.
4 years at an interest rate of 9\% p.a.
\$4000 is invested in a term deposit at a rate of 3\% per quarter compounded monthly. Find the value of the investment after 8 years.
\$3000 is invested in a term deposit at a rate of 1\% per month compounded quarterly. Find the value of the investment after 6 years.
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?
\$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?
Calculate how much is owed at the end of the following loan periods:
\$6000 is borrowed at a rate of 20\% p.a. compounded annually for 5 years.
Emma borrows \$7000 at a rate of 4.7\% p.a. compounded annually for 3 years.
\$8000 is borrowed at a rate of 5.4\% p.a. compounded semi-annually for 5 years.
For the compound interest formula A=P(1+i)^n, state the value of:
Calculate the final value of the loan A.
Calculate the interest owed on the loan I.
Assuming that a year has 52 weeks and 365 days, calculate how much is owed at the end of the following loan periods, given that no repayments are made:
\$4000 is borrowed at a rate of 2.8\% p.a. compounded quarterly for 3 years.
\$6000 is borrowed from a bank at a rate of 7.2\% p.a. compounded weekly for 5 years.
\$7000 is borrowed from a bank at a rate of 3.4\% p.a. compounded monthly for 6 years.
\$2000 is borrowed from a bank at a rate of 1.3\% p.a. compounded daily for 3 years.
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?
Sean borrows \$7000 at a rate of 5.5\% p.a. compounded weekly. If she pays off the loan in a lump sum at the end of 5 years, find how much interest she pays. Assume there are 52 weeks in a year.
Assuming that in a year there are 52 weeks and 365 days, calculate the amount of interest earned on the following investments:
Sally's investment of \$4200 earns interest at 2.7\% p.a. compounded quarterly over 13 years.
Sally's investment of \$3070 earns interest at 4.5\% p.a. compounded monthly over 7 years.
Han's investment of \$9110 earns interest at 3.2\% p.a. compounded weekly over 18 years.
Luke's investment of \$6220 earns interest at 2.8\% p.a. compounded daily over 11 years.
Buzz's investment of \$4920 earns interest at 5\% p.a. compounded semiannually over 2 years.
Sally's investment of \$8910 earns interest at 4\% p.a. compounded annually over 10 years.
Pauline borrows \$50\,000 at a rate of 5.4\% per annum. If she pays off the loan in a lump sum at the end of 7 years, find how much interest she pays if the interest is compounded:
Daily
Monthly
Quarterly
Emma wants to invest \$1400 at 5\% p.a for 5 years. She has two investment options, compounding quarterly or compounding monthly.
Calculate how much extra the investment is worth if it is compounded monthly rather than quarterly.
Maria has \$9000 to invest for 5 years and would like to know which investment plan to enter into out of the following three.
Plan 1: invest at 4.51\% p.a. interest, compounded monthly
Plan 2: invest at 6.16\% p.a. interest, compounded quarterly
Plan 3: invest at 5.50\% p.a. interest, compounded annually
Find the difference in investment return if Maria chooses the worst plan, compared to the best plan.
Mae's investment into a 20-year 2.33\% p.a. corporate bond grew to \$13\,600. Calculate the size of Mae's initial investment if interest was compounded:
Annually
Half-yearly
Quarterly
Monthly
Weekly, assuming there are 52 weeks in a year.
Daily, assuming there are 365 days in a year.
Katrina borrows \$6500 at a rate of 6.6\% p.a. compounded semi-annually. If she pays off the loan in a lump sum at the end of 5 years, find how much interest she pays.
Frank is working out the compound interest accumulated on his loan. He writes down the following working:
A = 6000\left(1+\dfrac{0.08}{4}\right)^{(7\times4)}
How much did he borrow in dollars?
What is the annual interest rate as a percentage?
Is the interest being compounded weekly, monthly, quarterly or annually?
For how many years is he accumulating interest?
How much interest does he pay?
The following spreadsheet shows the balance in a savings account where interest is compounded quarterly:
| A | B | C | D | |
|---|---|---|---|---|
| 1 | \text{Quarter} | \text{Balance at the beginning} \\ \text{of quarter} | \text{Interest} | \text{Balance at the end} \\ \text{of quarter} |
| 2 | 1 | \$100 | \$5100 | |
| 3 | 2 | \$5100 | \$5202.00 | |
| 4 | 3 | \$5202.00 | \$104.04 | |
| 5 | 4 | \$5306.04 | \$106.12 | \$5412.16 |
Calculate the quarterly interest rate, correct to two decimal places.
Complete the table.
The following spreadsheet shows the balance in a savings account, where interest is compounded monthly:
| A | B | C | D | |
|---|---|---|---|---|
| 1 | \text{Month} | \text{Balance at the beginning} \\ \text{of month} | \text{Interest} | \text{Balance at the end} \\ \text{of month} |
| 2 | \text{July} | \$3000 | \$30 | \$X |
| 3 | \text{August} | \$3030 | \$30.30 | \$3060.30 |
| 4 | \text{September} | \$3060.30 | \$Y | \$3090.90 |
| 5 | \text{October} | \$Z | \$30.91 | \$3121.81 |
| 6 | \text{November} | \$3121.21 | \$31.22 | \$3153.03 |
Complete the table.
The following spreadsheet shows the balance in a savings account, where interest is compounded monthly:
| A | B | C | D | |
|---|---|---|---|---|
| 1 | \text{Month} | \text{Balance at the beginning} \\ \text{of month} | \text{Interest} | \text{Balance at the end} \\ \text{of month} |
| 2 | \text{January} | \$1000 | \$20 | \$1020 |
| 3 | \text{February} | \$1020 | \$20.40 | \$1040.40 |
| 4 | \text{March} | \$1040.40 | \$20.81 | \$1061.21 |
| 5 | \text{April} | \$1061.21 | \$21.22 | \$1082.43 |
| 6 | \text{May} |
Use the numbers for January to calculate the monthly interest rate.
Complete the table for the month of May.
Use a spreadsheet to calculate the total amount of interest earned over the year.
The following spreadsheet shows the balance in a savings account in 2019, where interest is compounded quarterly:
| A | B | C | D | |
|---|---|---|---|---|
| 1 | \text{Quarter} | \text{Balance at the beginning} \\ \text{of quarter} | \text{Interest} | \text{Balance at the end} \\ \text{of quarter} |
| 2 | 1 | \$2000 | \$20 | \$2020 |
| 3 | 2 | \$2020 | \$20.20 | \$2040.20 |
| 4 | 3 | \$2040.20 | \$20.40 | \$2060.60 |
| 5 | 4 |
Calculate the quarterly interest rate.
Complete the table for quarter 4.
Use a spreadsheet to find how many quarters after the beginning of 2019 the balance will be double the initial investment of \$2000.