Consider the following investment strategies:
Investment strategy 1: \$6420 invested at 6\% p.a. compounded monthly.
Investment strategy 2: \$6420 invested at 6\% p.a. compounded weekly.
Investment strategy 3: \$6420 invested at 6\% p.a. compounded daily.
Find the value of Investment 1 after 18 years
Assuming 52 weeks in a year, find the value of Investment 2 after 18 years.
Assuming there are 365 days in a year, find the value of Investment 3 after 18 years.
Considering a range of investment strategies that differ only by the compounding frequency, determine whether the following statements are true:
An investment with a higher compounding frequency will yield a higher return.
An investment with a lower compounding frequency will yield a higher return.
The compounding frequency does not influence the return on the investment.
A \$150\,000 investment earns interest at 24\% p.a., compounded monthly over 10 years.
The following table shows the balance on a \$1000 investment for a particular number of periods, n:
| \text{Interest rate} \\ \text{per period} | n=115 | n=120 | n=125 | n=130 | n=135 |
|---|---|---|---|---|---|
| 1\% | 3140.20 | 3300.39 | 3468.74 | 3645.68 | 3831.65 |
| 2\% | 9750.34 | 10\,765.16 | 11\,885.61 | 13\,122.67 | 14\,488.49 |
| 3\% | 29\,942.00 | 34\,710.99 | 40\,239.55 | 46\,648.66 | 54078.59 |
| 4\% | 90\,956.56 | 110\,662.56 | 134\,637.93 | 163\,807.62 | 199\,297.02 |
| 5\% | 273\,381.67 | 348\,911.99 | 445\,309.93 | 568\,340.86 | 725\,362.96 |
Using the compound interest table, calculate:
the value of this investment, correct to the nearest cent.
the amount of interest earned, correct to the nearest cent.
Beth's investment into a 12-year 4.4\% p.a. corporate bond grew to \$13190. Calculate the size of Beth's initial investment if:
Interest was compounded annually.
Interest was compounded semiannually.
Interest was compounded quarterly.
Interest was compounded monthly.
Interest was compounded weekly.
Interest was compounded daily.
Consider the following investment strategies over 72 months:
Investment strategy 1: \$2600 invested in a simple interest account at 9.6\% per month.
Investment strategy 2: \$2600 invested at 4.1\% p.a. compounded annually.
Find the value of each of the following after 72 months.
Investment strategy 1
Investment strategy 2
Which option should be selected in order to maximise the return on the investment?
Robert plans to invest \$750 at 5.5\% p.a. compounded annually for 8 years. Jenny only has \$500 to invest, but wants to use the same strategy as Robert.
Find the value of each of the following after 8 years.
Robert’s investment
Jenny’s investment
Suppose the interest rate, compounding frequency, and investment period are the same. Determine whether the following statements are true:
An investment with a lower principal value will yield a higher return.
An investment with a higher principal value will yield a higher return.
The principal value does not influence the return on the investment.
Oliver has two savings accounts that have different interest rates.
If Account 1 initially has \$927 and interest is earned at 1.79\% p.a. compounded weekly, find the balance in the account after 40 weeks.
If Account 2 initially has \$234 and interest is earned at 5.59\% p.a. compounded weekly, find the balance in the account after 40 weeks.
Which account has returned the most interest after 40 weeks?
Consider the following investment strategies that have the same annual interest rate:
Investment strategy 1: \$881 invested at 2.11\% p.a. compounded annually.
Investment strategy 2: \$397 invested at 2.11\% p.a. compounded monthly.
Find the value of each of the following investments after 17 years.
Investment strategy 1
Investment strategy 2
Find the total interest earned from each of the following.
Investment strategy 1
Investment strategy 2
Which investment strategy has grown the most after 17 years?
A bank offers a two-stage investment strategy to attract new savings account customers. In Stage 1, interest is earned at 5.79\% p.a. compounded monthly for the first 12 months. In Stage 2, interest is earned at 1.21\% p.a. compounded weekly for the remainder of the life of the account. Assume there are 52 weeks in a year.
Find the balance after 1 year in a savings account that has an initial deposit of \$977.
Find the balance of the same account after 2 years.
Throughout which stage did the account earn the most interest?
Sandy and Tobias are each trying to save up to buy a new computer. Sandy deposits \$750 into a savings account offering 5.9\% p.a. compounded daily. Tobias opens an identical account, but only has \$310 to deposit.
Find the value of Sandy’s account after 4 years.
Find the value of Tobias’s account after 6 years.
If Sandy closes her account after 4 years, and Tobias closes his account after 6 years, whose account earned the most interest over its lifetime?
An investment firm has \$60\,000 to invest over a period of 21 months. They are considering which of the following investment strategies to pursue:
Investment strategy 1: interest earned at a rate of 1.1\% p.a. compounded weekly. Assume 52 weeks in a year.
Investment strategy 2: interest earned at a rate of 4.2\% p.a. compounded monthly.
Investment strategy 3: interest earned at a rate of 7.7\% p.a. compounded annually.
Find the value of each of the following investments after 21 months.
Investment 1
Investment 2
Investment 3
Which investment strategy will return the most interest after 21 months?
Grace wants to invest \$1300 at 2\% p.a for 6 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 \$1000 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 6.44\% p.a. interest, compounded quarterly
Plan 3: invest at 5.70\% p.a. interest, compounded annually
Which investment plan yields the highest return?