Maria invested \$1400 at 10\% p.a., compounded annually over 3 years. Without using the compound interest formula calculate:
The interest earned for the first year.
The balance after the first year.
The interest earned for the second year.
The balance after the second year.
The interest earned for the third year.
The balance after the third year.
The total amount of interest earned over the three years.
The interest as a percentage of the initial investment, correct to one decimal place.
The interest earned after three years if the investment was simple interest rather than compound interest.
Which type of interest is best for this investment and by how much is it better.
The following compound interest table shows the final value of a \$1000 investment, for various interest rates, compounded annually over various numbers of years:
| 10 \text{ years} | 15 \text{ years} | 20 \text{ years} | 25 \text{ years} | 30 \text{ years} | |
|---|---|---|---|---|---|
| r = 5\% \text{ p.a.} | 1628.89 | 1790.85 | 1967.15 | 2158.92 | 2367.36 |
| r = 6\% \text{ p.a.} | 2078.93 | 2396.56 | 2759.03 | 3172.17 | 3642.48 |
| r = 7\% \text{ p.a.} | 2653.30 | 3207.14 | 3869.68 | 4660.96 | 5604.41 |
| r = 8\% \text{ p.a.} | 3386.35 | 4291.87 | 5427.43 | 6848.48 | 8623.08 |
| r = 9\% \text{ p.a.} | 4321.94 | 5743.49 | 7612.26 | 10\,062.66 | 13\,267.68 |
If \$50\,000 is invested and earns interest at 6\% p.a. over 15 years, calculate:
The value of this investment.
The amount of interest earned.
Scott wants to have \$1500 at the end of 5 years. If the bank offers 2.3\% p.a. compounded annually, how much should he invest now?
Gwen takes out a loan to purchase a surround sound system. She makes 11 equal loan repayments. The total loan amount paid back is \$6600.
Calculate the amount of each repayment.
Lisa takes out a loan to purchase a small boat. She pays it back in equal monthly repayments over 6 years. The total loan amount paid back is \$55\,800.
Calculate the amount of each repayment.
The following compound interest table shows the final value of a \$1 investment, for various interest rates, compounded annually over various numbers of years:
| 10 \text{ years} | 11 \text{ years} | 12 \text{ years} | 13 \text{ years} | 14 \text{ years} | 15 \text{ years} | |
|---|---|---|---|---|---|---|
| r = 8\% | 2.1589 | 2.3316 | 2.5182 | 2.7196 | 2.9372 | 3.1722 |
| r = 9\% | 2.3674 | 2.5804 | 2.8127 | 3.0658 | 3.3417 | 3.6425 |
| r = 10\% | 2.5937 | 2.8531 | 3.1384 | 3.4523 | 3.7975 | 4.1772 |
| r = 11\% | 2.8394 | 3.1518 | 3.4985 | 3.8833 | 4.3104 | 4.7846 |
| r = 12\% | 3.1058 | 3.4785 | 3.896 | 4.3635 | 4.8871 | 5.4736 |
After how many years will a sum of money triple in value if it is invested at 10\% p.a., compounded annually?
Iain takes out a loan to purchase a jetski. He makes 15 equal loan repayments of \$5239.
Calculate the total amount paid back on the loan.
Dylan takes out a loan to purchase a property. He makes equal monthly loan repayments of \$4600 over 27 years to pay it off.
Calculate the total amount paid back on the loan.
Hermione takes out a loan of \$500 to purchase a computer. The loan earns interest at 8\% p.a. compounded annually. Repayments of \$100 are made annually. Calculate the amount she owes after her:
First repayment.
Second repayment.
Jimmy takes out a loan of \$700 to purchase a computer. The loan earns interest at 6\% p.a. compounded annually. Repayments of \$140 are made annually. Calculate the amount Jimmy still owes after his:
First repayment.
Second repayment.
Tara takes out a loan to purchase a property. The following image depicts the change of the loan over time:
How often is interest being added to the balance of the loan?
How often is Tara making a repayment on the loan?
Tracy takes out a loan to purchase a TV. The following image depicts the change of the loan over time:
How much did Tracy borrow?
How often is interest being added to the balance of the loan?
How often is Tracy making a repayment on the loan?
Joanne takes out a loan of \$54\,000 to purchase a plot of land. The loan earns interest at 2\% p.a. compounded annually. Repayments of \$864 are made annually.
How much interest is added to Joanne's loan in the first year?
Calculate the amount Joanne still owes after the first repayment.
Should Joanne continue to make annual payments of \$864? Explain your answer.
Suggest a better annual payment amount for Joanne's loan.
Dave takes out a loan of \$102\,000 to purchase an apartment. The loan accrues interest at 8\% p.a. compounded annually.
Will the loan be paid off in 3 years if \$2267 is repaid monthly?
Will the loan be paid off in 3 years if \$2834 is repaid monthly?
Will the loan be paid off in 3 years if \$3570 is repaid monthly?
Each of the following graphs represents a reducing balance loan in which the repayments are made annually. Match each of the graphs to one of the following scenarios:
Interest is added semi-annually and the loan is repaid in more than 3 years.
Interest is added quarterly and the loan is repaid in more than 3 years.
Interest is added every 6 months and the loan will never be repaid.
Interest is added annually and the loan is repaid in 3 years.
A study abroad loan of \$10\,200 accrues interest at 4.8\% p.a. compounded monthly. Repayments of \$3060 are made half yearly. Below is a table documenting the repayment of the loan.
| \text{Time }\\\text{period }\\ (n) | \text{Balance at }\\\text{beginning }\\\text{ of time period }(\$) | \text{Interest}\\\text{charged }\\(\$) | \text{Repayment}\\\text{this period }\\(\$) | \text{Balance at end }\\\text{end of time period }\\(\$) |
|---|---|---|---|---|
| 1 | 10\,200 | 247.26 | 3060 | 7387.26 |
| 2 | 7387.26 | 179.08 | 3060 | 4506.34 |
| 3 | 4 506.31 | 109.24 | 3060 | 1555.58 |
| 4 | 1 555.58 | 37.71 | 1593.29 | 0 |
Determine whether the following are methods of finding the total loan amount:
The sum of the balances at the end of each period.
The sum of the interests for each period plus the initial loan.
The sum of the loan repayments.
The initial loan amount multiplied by the interest rate.
What is the total repayment on the loan?
A car loan of \$6000 earns interest at 8\% p.a. compounded annually. Repayments of \$720 are made annually.
Complete the following table which tracks the loan over the first three years:
| \text{Time period} \\ (n) | \text{Value at beginning} \\ \text{of time period} | \text{Interest at end} \\ \text{of time period} | \text{Repayment} \\ \text{this period} | \text{Amount at} \\ \text{end of time period} |
|---|---|---|---|---|
| 1 | \$6000 | |||
| 2 | \$460.80 | \$720 | ||
| 3 | \$5500.80 | \$720 |
A loan of \$54\,000 earns interest at 5.4\% p.a. compounded monthly. Repayments of \$1500 are made monthly.
Complete the following table which tracks the loan amount over the first three months:
| \text{Time period} \\ (n) | \text{Value at beginning} \\ \text{of time period} | \text{Interest at end} \\ \text{of time period} | \text{Repayment} \\ \text{this period} | \text{Amount at} \\ \text{end of time period} |
|---|---|---|---|---|
| 1 | \$243.00 | \$1500 | \$52\,743 | |
| 2 | \$237.34 | |||
| 3 | \$51\,480.34 | \$231.66 | \$1500 |
A small loan of \$4500 to pay for a holiday earns interest at 4\% p.a. compounded annually. Repayments of \$2000 are made annually.
Complete the following table which tracks the loan amount over three years:
| \text{Time} \\ \text{period } (n) | \text{Value at beginning} \\ \text{of time period} | \text{Interest at end} \\ \text{of time period} | \text{Repayment} \\ \text{this period} | \text{Amount at} \\ \text{end of time period} |
|---|---|---|---|---|
| 1 | \$4500 | \$2000 | ||
| 2 | \$107.20 | |||
| 3 | \$787.20 | \$0 |
Why is the repayment in the third year smaller than the other repayments?
Calculate the total loan amount paid.
A study abroad loan of \$13\,600 earns interest at 2.4\% p.a. compounded monthly. Repayments of \$4080 are made either half-yearly or yearly.
Complete the following table which tracks the repayment of the loan with half-yearly payments:
| \text{Time} \\ \text{period }(n) | \text{Value at beginning} \\ \text{of time period} | \text{Interest at end} \\ \text{of time period} | \text{Repayment} \\ \text{this period} | \text{Amount at} \\ \text{end of time period} |
|---|---|---|---|---|
| 1 | \$13\,600 | \$164.02 | \$4080 | |
| 2 | \$9684.02 | \$116.79 | ||
| 3 | \$5720.81 | \$68.99 | \$4080 | |
| 4 | \$0 |
What is the total loan amount paid if making half yearly repayments?
Complete the following table that tracks the repayment of the loan with yearly payments:
| \text{Time} \\ \text{period }(n) | \text{Value at beginning} \\ \text{of time period} | \text{Interest at end} \\ \text{of time period} | \text{Repayment} \\ \text{this period} | \text{Amount at} \\ \text{end of time period} |
|---|---|---|---|---|
| 1 | \$13\,600 | \$330.01 | \$8160 | |
| 2 | \$5770.01 | \$140.01 |
What is the total loan amount paid if making yearly repayments?
What is the better payment option in order to reduce the total amount paid?