The following financial table displays the annual repayments on a \$1000 loan:
| \text{Annual interest rate} | 10 \\ \text{years} | 15 \\ \text{years} | 20 \\ \text{years} | 25 \\ \text{years} | 30 \\ \text{years} |
|---|---|---|---|---|---|
| 5\% | 129.50 | 96.34 | 80.24 | 70.95 | 65.05 |
| 6\% | 135.87 | 102.96 | 87.18 | 78.23 | 72.65 |
| 7\% | 142.38 | 109.79 | 94.39 | 85.81 | 80.59 |
| 8\% | 149.03 | 116.83 | 101.85 | 93.68 | 88.83 |
| 9\% | 155.82 | 124.06 | 109.55 | 101.81 | 97.34 |
| 10\% | 162.75 | 131.47 | 117.46 | 110.17 | 106.08 |
Calculate the annual installments needed to pay off a \$110\,000 home loan at 7\% p.a. reducible interest if the installments are to be paid in equal amounts over 15 years.
The following financial table displays the monthly repayments on a \$1000 loan:
| \text{Annual interest rate} | 10 \\ \text{years} | 15 \\ \text{years} | 20 \\ \text{years} | 25 \\ \text{years} | 30 \\ \text{years} |
|---|---|---|---|---|---|
| 3\% | 9.66 | 6.91 | 5.55 | 4.74 | 4.22 |
| 4\% | 10.12 | 7.40 | 6.06 | 5.28 | 4.77 |
| 5\% | 10.61 | 7.91 | 6.60 | 5.85 | 5.37 |
| 6\% | 11.10 | 8.44 | 7.16 | 6.44 | 6.00 |
| 7\% | 11.61 | 8.99 | 7.75 | 7.07 | 6.65 |
| 8\% | 12.17 | 9.56 | 8.36 | 7.72 | 7.38 |
Calculate the monthly instalments required to pay off a 25-year loan of \$1000 at 4\% p.a. monthly reducible interest.
The following financial table displays the monthly instalments required to save \$1000:
| \text{Annual interest rate} | 5 \\ \text{years} | 10 \\ \text{years} | 15 \\ \text{years} | 20 \\ \text{years} | 25 \\ \text{years} |
|---|---|---|---|---|---|
| 1\% | 16.26 | 7.93 | 5.15 | 3.77 | 2.94 |
| 2\% | 15.86 | 7.53 | 4.77 | 3.39 | 2.57 |
| 3\% | 15.47 | 7.16 | 4.41 | 3.05 | 2.24 |
| 4\% | 15.08 | 6.79 | 4.06 | 2.73 | 1.95 |
| 5\% | 14.70 | 6.44 | 3.74 | 2.43 | 1.68 |
| 6\% | 14.33 | 6.10 | 3.44 | 2.16 | 1.44 |
Calculate the monthly instalments required to save \$50\,000 in 15 years if the savings account earns 3\% interest per annum, compounded monthly.
The following financial table displays the monthly repayments on a \$1000 loan:
| \text{Annual interest rate} | 10 \\ \text{years} | 15 \\ \text{years} | 20 \\ \text{years} | 25 \\ \text{years} | 30 \\ \text{years} |
|---|---|---|---|---|---|
| 5\% | 10.61 | 7.91 | 6.60 | 5.85 | 5.37 |
| 6\% | 11.10 | 8.44 | 7.16 | 6.44 | 6.00 |
| 7\% | 11.61 | 8.99 | 7.75 | 7.07 | 6.65 |
| 8\% | 12.13 | 9.56 | 8.36 | 7.72 | 7.34 |
| 9\% | 12.67 | 10.14 | 9.00 | 8.39 | 8.05 |
| 10\% | 13.22 | 10.75 | 9.65 | 9.09 | 8.78 |
Calculate the monthly instalments required to pay off a 15-year loan of \$200\,000 at 7\% p.a. monthly reducible interest.
The following financial table displays the monthly repayments on a \$1000 loan:
| \text{Annual interest rate} | 5 \\ \text{years} | 10 \\ \text{years} | 15 \\ \text{years} | 20 \\ \text{years} | 25 \\ \text{years} |
|---|---|---|---|---|---|
| 3\% | 17.97 | 9.66 | 6.91 | 5.55 | 4.74 |
| 4\% | 18.42 | 10.12 | 7.40 | 6.06 | 5.28 |
| 5\% | 18.87 | 10.61 | 7.91 | 6.60 | 5.85 |
| 6\% | 19.33 | 11.10 | 8.44 | 7.16 | 6.44 |
| 7\% | 19.80 | 11.61 | 8.99 | 7.75 | 7.07 |
| 8\% | 20.28 | 12.13 | 9.56 | 8.36 | 7.72 |
Amelia received a 5-year \$120\,000 loan at 3\% p.a. monthly reducible interest. Find:
The amount of each monthly instalment.
The total repayments.
The interest on the loan.
The total interest as a percentage of the principal loan, correct to two decimal places.
The following financial table displays the monthly instalments required to save \$1000:
| \text{Annual interest rate} | 10 \\ \text{years} | 15 \\ \text{years} | 20 \\ \text{years} | 25 \\ \text{years} | 30 \\ \text{years} |
|---|---|---|---|---|---|
| 3\% | 7.16 | 4.41 | 3.05 | 2.24 | 1.72 |
| 4\% | 6.79 | 4.06 | 2.73 | 1.95 | 1.44 |
| 5\% | 6.44 | 3.74 | 2.43 | 1.68 | 1.20 |
| 6\% | 6.10 | 3.44 | 2.16 | 1.44 | 1.00 |
| 7\% | 5.78 | 3.15 | 1.92 | 1.23 | 0.82 |
| 8\% | 5.47 | 2.89 | 1.70 | 1.05 | 0.67 |
The interest rate on a savings account is 4\% per annum, compounded monthly. Vincent can afford to save \$300 per month. How long will it take him to save \$143\,000?
The following financial table displays the monthly repayments on a \$1000 loan:
| \text{Annual interest rate} | 5 \\ \text{years} | 10 \\ \text{years} | 15 \\ \text{years} | 20 \\ \text{years} | 25 \\ \text{years} |
|---|---|---|---|---|---|
| 4\% | 18.42 | 10.12 | 7.40 | 6.06 | 5.28 |
| 5\% | 18.87 | 10.61 | 7.91 | 6.60 | 5.85 |
| 6\% | 19.33 | 11.10 | 8.44 | 7.16 | 6.44 |
| 7\% | 19.80 | 11.61 | 8.99 | 7.75 | 7.07 |
| 8\% | 20.28 | 12.13 | 9.56 | 8.36 | 7.72 |
| 9\% | 20.76 | 12.67 | 10.14 | 9.00 | 8.39 |
Luke received a 5-year loan at 4\% p.a. monthly reducible interest. His total repayments were \$221\,040.
Calculate the amount of each monthly instalment.
Find the amount of the loan.
The following financial table displays the monthly repayments on a \$1000 loan:
| \text{Annual interest rate} | 20 \\ \text{years} | 25 \\ \text{years} | 30 \\ \text{years} | 35 \\ \text{years} | 40 \\ \text{years} |
|---|---|---|---|---|---|
| 3\% | 5.55 | 4.74 | 4.22 | 3.85 | 3.58 |
| 4\% | 6.06 | 5.28 | 4.77 | 4.43 | 4.18 |
| 5\% | 6.60 | 5.85 | 5.37 | 5.05 | 4.82 |
| 6\% | 7.16 | 6.44 | 6.00 | 5.70 | 5.50 |
| 7\% | 7.75 | 7.07 | 6.65 | 6.39 | 6.21 |
| 8\% | 8.36 | 7.72 | 7.34 | 7.10 | 6.95 |
Han received a 25-year \$71\,000 loan at 5\% p.a. monthly reducible interest. If the term of the loan was reduced to 20 years, calculate:
The size of the monthly instalment when the term of the loan is 25 years.
The total amount repaid over 25 years.
The interest paid over 25 years.
The total amount repaid over a reduced term of 20 years.
The interest paid over the 20-year term.
The interest saved from a 5-year reduction in the term of the loan.
The following financial table displays the monthly instalments required to save \$1000:
| \text{Annual interest rate} | 15 \\ \text{years} | 20 \\ \text{years} | 25 \\ \text{years} | 30 \\ \text{years} | 35 \\ \text{years} |
|---|---|---|---|---|---|
| 1\% | 5.15 | 3.77 | 2.94 | 2.38 | 1.99 |
| 2\% | 4.77 | 3.39 | 2.57 | 2.03 | 1.65 |
| 3\% | 4.41 | 3.05 | 2.24 | 1.72 | 1.35 |
| 4\% | 4.06 | 2.73 | 1.95 | 1.44 | 1.09 |
| 5\% | 3.74 | 2.43 | 1.68 | 1.20 | 0.88 |
| 6\% | 3.44 | 2.16 | 1.44 | 1.00 | 0.70 |
Calculate the monthly instalments required to save \$110\,000 in 30 years if the savings account earns 5\% interest per annum, compounded monthly.
If instead of making consistent payments to an annuity, a single deposit was made into the same account at the start of the investment, how much must be invested in order to end up with \$110\,000 after 30 years?
The following financial table displays the monthly repayments on a \$1000 loan:
| \text{Annual interest rate} | 15 \\ \text{years} | 20 \\ \text{years} | 25 \\ \text{years} | 30 \\ \text{years} | 35 \\ \text{years} |
|---|---|---|---|---|---|
| 2\% | 6.44 | 5.06 | 4.24 | 3.70 | 3.31 |
| 3\% | 6.91 | 5.55 | 4.74 | 4.22 | 3.85 |
| 4\% | 7.40 | 6.06 | 5.28 | 4.77 | 4.43 |
| 5\% | 7.91 | 6.60 | 5.85 | 5.37 | 5.05 |
| 6\% | 8.44 | 7.16 | 6.44 | 6.00 | 5.70 |
| 7\% | 8.99 | 7.75 | 7.07 | 6.65 | 6.39 |
Mae received a 30-year \$89\,000 loan at 2\% p.a. monthly reducible interest. If the term of the loan was reduced to 25 years, calculate:
The amount of each monthly instalment over a 30-year term.
The monthly instalment needed for a 25-year term.
The amount saved, from this 5-year reduction in the term of the loan.
The following financial table displays the monthly repayments on a \$1000 loan:
| \text{Annual interest rate} | 10 \\ \text{years} | 15 \\ \text{years} | 20 \\ \text{years} | 25 \\ \text{years} | 30 \\ \text{years} |
|---|---|---|---|---|---|
| 4\% | 10.12 | 7.40 | 6.06 | 5.28 | 4.77 |
| 5\% | 10.61 | 7.91 | 6.60 | 5.85 | 5.37 |
| 6\% | 11.10 | 8.44 | 7.16 | 6.44 | 6.00 |
| 7\% | 11.61 | 8.99 | 7.75 | 7.07 | 6.65 |
| 8\% | 12.13 | 9.56 | 8.36 | 7.72 | 7.34 |
| 9\% | 12.67 | 10.14 | 9.00 | 8.39 | 8.05 |
Neil received a 10-year \$130\,000 loan at 6\% p.a. monthly reducible interest. If the interest rate was increased to 7\% p.a., find the increase in the total repayments needed to clear the debt.
The following financial table displays the monthly repayments on a \$1000 loan:
| \text{Annual interest rate} | 15 \\ \text{years} | 20 \\ \text{years} | 25 \\ \text{years} | 30 \\ \text{years} | 35 \\ \text{years} |
|---|---|---|---|---|---|
| 3\% | 6.91 | 5.55 | 4.74 | 4.22 | 3.85 |
| 4\% | 7.40 | 6.06 | 5.28 | 4.77 | 4.43 |
| 5\% | 7.91 | 6.60 | 5.85 | 5.37 | 5.05 |
| 6\% | 8.44 | 7.16 | 6.44 | 6.00 | 5.70 |
| 7\% | 8.99 | 7.75 | 7.07 | 6.65 | 6.39 |
| 8\% | 9.56 | 8.36 | 7.72 | 7.34 | 7.10 |
Mae received a 15-year \$60\,000 loan at 6\% p.a. monthly reducible interest. If the interest rate fell to 5\% p.a., find the decrease in the total repayments needed to clear the debt.
Use the table to find the future value of an annuity in which \$6000 is invested every year for 4 years at 15\% p.a. with interest compounded annually.
| \text{Period} | 11\% \\ \text{per year} | 12\% \\ \text{per year} | 13\% \\ \text{per year} | 14\% \\ \text{per year} | 15\% \\ \text{per year} |
|---|---|---|---|---|---|
| 0 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
| 1 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |
| 2 | 2.1100 | 2.1200 | 2.1300 | 2.1400 | 2.1500 |
| 3 | 3.3421 | 3.3744 | 3.4069 | 3.4396 | 3.4725 |
| 4 | 4.7097 | 4.7793 | 4.8498 | 4.9211 | 4.9934 |
| 5 | 6.2278 | 6.3528 | 6.4803 | 6.6101 | 6.7424 |
Use the table to find the interest generated on an annuity in which \$3100 is invested every year for 7 years at 15\% p.a. with interest compounded annually.
| \text{Period} | 14.5\% \\ \text{per year} | 15\% \\ \text{per year} | 15.5\% \\ \text{per year} | 16\% \\ \text{per year} | 16.5\% \\ \text{per year} |
|---|---|---|---|---|---|
| 3 | 3.4560 | 3.4725 | 3.4890 | 3.5056 | 3.5222 |
| 4 | 4.9571 | 4.9934 | 5.0298 | 5.0665 | 5.1034 |
| 5 | 6.6759 | 6.7424 | 6.8094 | 6.8771 | 6.9455 |
| 6 | 8.6439 | 8.7537 | 8.8649 | 8.9775 | 9.0915 |
| 7 | 10.8973 | 11.0668 | 11.2390 | 11.4139 | 11.5915 |
| 8 | 13.4774 | 13.7268 | 13.9810 | 14.2401 | 14.5041 |
Use the table to find the future value of an annuity in which \$2500 is invested every 3 months for 5 years at 15\% p.a. with interest compounded quarterly.
| \text{Period} | 2.75\% \\ \text{per quarter} | 3.25\% \\ \text{per quarter} | 3.75\% \\ \text{per quarter} | 4.25\% \\ \text{per quarter} | 4.75\% \\ \text{per quarter} |
|---|---|---|---|---|---|
| 20 | 26.1974 | 27.5642 | 29.0174 | 30.5625 | 32.2056 |
| 21 | 27.9178 | 29.4601 | 31.1055 | 32.8614 | 34.7354 |
| 22 | 29.6856 | 31.4175 | 33.2720 | 35.2580 | 37.3853 |
| 23 | 31.5019 | 33.4386 | 35.5197 | 37.7565 | 40.1611 |
| 24 | 33.3682 | 35.5254 | 37.8517 | 40.3611 | 43.0688 |
| 25 | 35.2858 | 37.6799 | 40.2711 | 43.0765 | 46.1146 |
Use the table to find the interest generated on an annuity in which \$2700 is invested every 3 months for 2 years at 9\% p.a. with interest compounded quarterly.
| \text{Period} | 2.25\% \\ \text{per quarter} | 2.75\% \\ \text{per quarter} | 3.25\% \\ \text{per quarter} | 3.75\% \\ \text{per quarter} | 4.25\% \\ \text{per quarter} |
|---|---|---|---|---|---|
| 8 | 8.6592 | 8.8138 | 8.9716 | 9.1326 | 9.2967 |
| 9 | 9.8540 | 10.0562 | 10.2632 | 10.4750 | 10.6918 |
| 10 | 11.0757 | 11.3328 | 11.5967 | 11.8678 | 12.1462 |
| 11 | 12.3249 | 12.6444 | 12.9736 | 13.3129 | 13.6624 |
| 12 | 13.6022 | 13.9921 | 14.3953 | 14.8121 | 15.2431 |
| 13 | 14.9083 | 15.3769 | 15.8631 | 16.3676 | 16.8909 |
Han is hoping to save up \$18\,347 for when he retires in 12 years. In order to achieve this goal, he deposits \$10 into his superannuation fund every week. The fund generates an average return of 15.6\% p.a., compounded weekly.
| \text{Period} | 0.2\% \\ \text{per week} | 0.3\% \\ \text{per week} | 0.4\% \\ \text{per week} | 0.5\% \\ \text{per week} | 0.6\% \\ \text{per week} |
|---|---|---|---|---|---|
| 620 | 1225.6684 | 1801.9584 | 2720.5848 | 4205.4298 | 6634.7095 |
| 621 | 1229.1198 | 1808.3643 | 2732.4671 | 4227.4569 | 6675.5178 |
| 622 | 1232.5780 | 1814.7894 | 2744.3970 | 4249.5942 | 6716.5709 |
| 623 | 1236.0432 | 1821.2337 | 2756.3746 | 4271.8422 | 6757.8703 |
| 624 | 1239.5152 | 1827.6974 | 2768.4001 | 4294.2014 | 6799.4175 |
| 625 | 1242.9943 | 1834.1805 | 2780.4737 | 4316.6724 | 6841.2140 |
Using the table of future value interest factors, how much will Han have saved up by the time he retires?
Will he reach his savings goal?
Use the table to find the contribution Mae needs to deposit into her savings account every 3 months, which pays 12\% p.a. with interest compounded quarterly, in order to reach her savings goal of \$42576 in 3 years. Round your answer to the nearest dollar.
| \text{Period} | 2\% \\ \text{per quarter} | 2.5\% \\ \text{per quarter} | 3\% \\ \text{per quarter} | 3.5\% \\ \text{per quarter} | 4\% \\ \text{per quarter} |
|---|---|---|---|---|---|
| 10 | 10.9497 | 11.2034 | 11.4639 | 11.7314 | 12.0061 |
| 11 | 12.1687 | 12.4835 | 12.8078 | 13.1420 | 13.4864 |
| 12 | 13.4121 | 13.7956 | 14.1920 | 14.6020 | 15.0258 |
| 13 | 14.6803 | 15.1404 | 15.6178 | 16.1130 | 16.6268 |
| 14 | 15.9739 | 16.5190 | 17.0863 | 17.6770 | 18.2919 |
| 15 | 17.2934 | 17.9319 | 18.5989 | 19.2957 | 20.0236 |
Use the table to find the present value of an annuity in which \$7000 is invested every year for 9 years at 3\% p.a. with interest compounded annually.
| \text{Period} | 1\% \\ \text{per year} | 1.5\% \\ \text{per year} | 2\% \\ \text{per year} | 2.5\% \\ \text{per year} | 3\% \\ \text{per year} |
|---|---|---|---|---|---|
| 8 | 7.6517 | 7.4859 | 7.3255 | 7.1701 | 7.0197 |
| 9 | 8.5660 | 8.3605 | 8.1622 | 7.9709 | 7.7861 |
| 10 | 9.4713 | 9.2222 | 8.9826 | 8.7521 | 8.5302 |
| 11 | 10.3676 | 10.0711 | 9.7868 | 9.5142 | 9.2526 |
| 12 | 11.2551 | 10.9075 | 10.5753 | 10.2578 | 9.9540 |
| 13 | 12.1337 | 11.7315 | 11.3484 | 10.9832 | 10.6350 |
Use the table to find the present value of an annuity in which \$2800 is invested every 6 months for 7 years at 12\% p.a. with interest compounded semi-annually.
| \text{Period} | 5.5\% \\ \text{per 6 months} | 6\% \\ \text{per 6 months} | 6.5\% \\ \text{per 6 months} | 7\% \\ \text{per 6 months} | 7.5\% \\ \text{per 6 months} |
|---|---|---|---|---|---|
| 11 | 8.0925 | 7.8869 | 7.6890 | 7.4987 | 7.3154 |
| 12 | 8.6185 | 8.3838 | 8.1587 | 7.9427 | 7.7353 |
| 13 | 9.1171 | 8.8527 | 8.5997 | 8.3577 | 8.1258 |
| 14 | 9.5896 | 9.2950 | 9.0138 | 8.7455 | 8.4892 |
| 15 | 10.0376 | 9.7122 | 9.4027 | 9.1079 | 8.8271 |
| 16 | 10.4622 | 10.1059 | 9.7678 | 9.4466 | 9.1415 |
Use the table to find the contribution Beth needs to deposit into her savings account every 3 months, which pays 9\% p.a. with interest compounded quarterly, in order to obtain an amount in 6 years with a present value of \$5516.71.
| \text{Period} | 0.25\% \\ \text{per quarter} | 0.75\% \\ \text{per quarter} | 1.25\% \\ \text{per quarter} | 1.75\% \\ \text{per quarter} | 2.25\% \\ \text{per quarter} |
|---|---|---|---|---|---|
| 20 | 19.4845 | 18.5080 | 17.5993 | 16.7529 | 15.9637 |
| 21 | 20.4334 | 19.3628 | 18.3697 | 17.4475 | 16.5904 |
| 22 | 21.3800 | 20.2112 | 19.1306 | 18.1303 | 17.2034 |
| 23 | 22.3241 | 21.0533 | 19.8820 | 18.8012 | 17.8028 |
| 24 | 23.2660 | 21.8891 | 20.6242 | 19.4607 | 18.3890 |
| 25 | 24.2055 | 22.7188 | 21.3573 | 20.1088 | 18.9624 |
Rosey buys a car for \$21\,000 and repays it over 4 years through equal monthly instalments. She pays a 10 \% deposit and interest is charged at 9 \% p.a. on the reducing balance loan.
| N | 0.6 \% \\ \text{per month} | 0.65 \% \\ \text{per month} | 0.70 \% \\ \text{per month} | 0.75 \% \\ \text{per month} | 0.80 \% \\ \text{per month} | 0.85 \% \\ \text{per month} |
|---|---|---|---|---|---|---|
| 45 | 39.33406 | 38.90738 | 38.48712 | 38.07318 | 37.66545 | 37.26383 |
| 46 | 40.09350 | 39.64965 | 39.21263 | 38.78231 | 38.35859 | 37.94133 |
| 47 | 40.84841 | 40.38714 | 39.93310 | 39.48617 | 39.04622 | 38.61311 |
| 48 | 41.59882 | 41.11986 | 40.64856 | 40.18478 | 39.72839 | 39.27924 |
| 49 | 42.34475 | 41.84785 | 41.35905 | 40.87820 | 40.40515 | 39.93975 |
| 50 | 43.08623 | 42.57113 | 42.06459 | 41.56645 | 41.07653 | 40.59470 |
Find the monthly repayment P that Rosey must pay to to complete the loan after 4 years.
Calculate the total interest paid over the life of the loan.
The table gives the present value interest factors for annuity of \$1 per period, for various interest rates r and numbers of periods N:
| N | 0.75 \% \\ \text{per month} | 0.80 \% \\ \text{per month} | 0.85 \% \\ \text{per month} | 0.90 \% \\ \text{per month} | 0.95 \% \\ \text{per month} |
|---|---|---|---|---|---|
| r | 0.0075 | 0.0080 | 0.0085 | 0.0090 | 0.0095 |
| 70 | 54.30462 | 53.43960 | 52.59397 | 51.76724 | 50.95891 |
| 71 | 54.89293 | 54.00754 | 53.14226 | 52.29657 | 51.46995 |
| 72 | 55.47685 | 54.57097 | 53.68593 | 52.82118 | 52.47764 |
| 73 | 56.05643 | 55.12993 | 54.22502 | 53.34111 | 52.47764 |
| 74 | 56.63169 | 55.68446 | 54.75957 | 53.85641 | 52.97438 |
Tom plans to invest \$200 per month for 74 months. His investment will earn interest at a rate of 0.0080 (as a decimal) per month. Calculate the present value of the annuity.
Hannah has a loan of \$21\,500 and will be repaid in equal monthly repayments over 6 years. The interest rate on her loan is 10.8 \% per annum. Find the monthly repayment P.
The table gives the present value interest factors for annuity of \$1 per period:
| \text{Period} | 1 \% \text{ p.a.} | 2 \% \text{ p.a.} | 4 \% \text{ p.a.} | 6 \% \text{ p.a.} |
|---|---|---|---|---|
| 1 | 0.9901 | 0.9804 | 0.9615 | 0.9434 |
| 2 | 1.9704 | 1.9416 | 1.8861 | 1.8334 |
| 3 | 2.9410 | 2.8839 | 2.7751 | 2.6730 |
| 4 | 3.9020 | 3.8077 | 3.6299 | 3.4651 |
Tina pays \$3000 into an annuity at the end of each year for 4 years at 2 \% p.a. compounded annually. Find the present value of her annuity.
If Jack pays \$6000 into an annuity at the end of each year for 2 years at 4 \% p.a. compounded annually. Is he better off than Tina?
AMS Bank of offers two investment opportunities to investors:
Option 1: 6.86\% p.a. simple interest for 10 years.
Option 2: 6.76\% p.a. compound interest for 6 years, compounding semiannually.
On an investment of \$1000, find the interest earned for Option 1.
On an investment of \$1000, find the interest earned for Option 2.
Find the effective annual interest rate for Option 2, to two decimal places.
Which of the two investment opportunities has the larger effective annual interest rate?
Complete the following sentences relating to annuities:
Contributions are made:
At regular time intervals.
Whenever you feel like it.
The interest is paid at:
The end of each time period.
The beginning of each time period.
The future value of an annuity is:
Equal to the sum of the individual contributions.
Greater than the sum of the individual contributions.
You need to take out a loan and you have the following interest rate options:
Option 1: 1.9\% p.a. compounding semi-annually
Option 2: 1.5\% p.a. compounding quarterly
Which option would you choose? Use calculations and reasoning to explain your answer.
Two different lending institutions are offering different rates on their loans:
Betta Bank is offering 4.4\% p.a. compounding monthly.
Lucky Lending is offering 4.2\% p.a. compounding quarterly.
What is the effective rate of Betta Bank correct to two decimal places?
What is the effective rate of Lucky Lending correct to two decimal places?
Which institution has the better offer? Explain your answer.
Dave's investment of \$17\,380 earned 6.2\% p.a. simple interest for the first 5 years and 0.29\% p.a. compound interest for the next 8 years, compounded daily.
Calculate the value of the investment after 5 years.
Calculate the final value of the investment.
Calculate the total amount of interest earned.
Calculate the average amount of interest earned per year.
Express the average interest per year as a percentage of the original investment. Round your answer to two decimal places.
Maria has \$7000 to invest for 4 years and would like to know which investment plan to enter into out of the following three:
Plan 1: Invest at 4.98\% p.a. interest, compounded monthly.
Plan 2: Invest at 6.63\% p.a. interest, compounded quarterly.
Plan 3: Invest at 5.90\% p.a. interest, compounded annually.
Determine which investment plan yields the highest return, showing calculations to support your answer.