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+r)^t, 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+r)^t, 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+r)^t, 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+r)^t, 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+r)^t, 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+r)^t, 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+r)^t, 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 the value of the investment if it is compounded quarterly.
Calculate the value of the investment if it is compounded 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
Calculate the future value of the investment under Plan 1.
Calculate the future value of the investment under Plan 2.
Calculate the future value of the investment under Plan 3.
Which investment plan yields the highest return?
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 in 2011, 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 2011 the balance will be double the initial investment of \$2000.
The following spreadsheet shows the balance in a savings account in 2011, 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 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 in 2013, 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.