A \$2400 investment earns interest at 4\% p.a. over 7 years.
Determine whether the following compounding periods would earn the greatest interest:
annually
quarterly
monthly
weekly
Calculate the value of this investment if compounded quarterly.
Calculate the final value of each of the following investments:
A \$9560 investment earns interest at 4\% p.a. compounded monthly over 9 years.
A \$9640 investment earns interest at 4.7\% p.a. compounded weekly over 4 years.
A \$2000 investment earns interest at 2.2\% p.a. compounded daily over 16 years.
A \$5510 investment earns interest at 3.7\% p.a. compounded weekly over 6 years.
A \$7000 investment earns interest at 3.9\% p.a. compounded monthly over 13 years.
Calculate how much is owed at the end of the following loan periods:
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.
Steph wants to invest \$2000 at 5\% p.a for 6 years. She has two investment options, compounding quarterly or compounding monthly, and wants to find the difference in the final investment values of these two options.
Calculate the value of the investment if it is compounded quarterly.
Calculate the value of the investment if it is compounded monthly.
Hence, calculate how much extra the investment is worth if it is compounded monthly rather than quarterly.
Maria has \$2000 to invest for 2 years and would like to know which investment plan to enter into given the following options:
Plan 1: invest at 5.18\% p.a. interest, compounded monthly
Plan 2: invest at 6.54\% p.a. interest, compounded quarterly
Plan 3: invest at 5.80\% 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?
For each investment below, calculate the total amount of interest earned:
Mae’s investment of \$4430 earns interest at 2.9\% p.a. compounded quarterly over 18 years.
Beth’s investment of \$7520 earns interest at 4.1\% p.a. compounded monthly over 20 years.
Mia’s investment of \$1040 earns interest at 4\% p.a. compounded weekly over 18 years.
Han’s investment of \$2470 earns interest at 2.6\% p.a. compounded semi-annually over 4 years.
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.
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
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?
A \$110\,000 investment earns interest at 4\% p.a. compounded semi-annually over 5 years. The compound interest table shows the future value of a \$1000 investment compounded at various interest rates and over a certain number of periods.
| \text{Interest rate} \\ \text{per period} | 10\text{ years} | 20\text{ years} | 30\text{ years} | 40\text{ years} | 50\text{ years} |
|---|---|---|---|---|---|
| 0.5\% | 1051.14 | 1104.90 | 1161.40 | 1220.79 | 1283.23 |
| 1\% | 1104.62 | 1220.19 | 1347.85 | 1488.86 | 1644.63 |
| 1.5\% | 1160.54 | 1346.86 | 1563.08 | 1814.02 | 2105.24 |
| 2\% | 1218.99 | 1485.95 | 1811.36 | 2208.04 | 2691.59 |
| 2.5\% | 1280.08 | 1638.62 | 2097.57 | 2685.06 | 3437.11 |
Using the table, calculate:
The future value of this investment.
The total amount of interest earned.
A bank offers the following rates on investment accounts:
Option 1: 4\% p.a. compounded annually
Option 2: 3.94\% p.a. compounded quarterly
The bank is looking to also offer a third option, compounding semi-annually. Comment on the rate they would need to offer so that a \$1000 investment results in the same returns across all three options.