16.04 Compound interest
\$3900 is invested for three years at a rate of 10\% p.a., compounded annually.
Complete the table below to determine the final value of the investment:
| Balance at beginning of year | Interest earned | |
|---|---|---|
| First year | \$3900 | \$390 |
| Second year | \$4290 | \$429 |
| Third year | ||
| Fourth year | - |
Calculate the total interest earned over the three years.
\$3700 is invested for three years at a rate of 7\% p.a., compounded annually.
Complete the table below to determine the final value of the investment:
| Balance at beginning of year | Interest earned | |
|---|---|---|
| First year | \$3700 | \$259 |
| Second year | \$3959 | \$277.13 |
| Third year | ||
| Fourth year | - |
Calculate the total interest earned over the three years.
\$3000 is invested at 4\% p.a., compounded annually. The table below tracks the growth of the principal over three years:
| Time Period (years) | Value at beginning of time period | Value at end of time period | Interest earned in time period |
|---|---|---|---|
| 1 | \$3000 | A | B |
| 2 | C | \$3244.80 | D |
| 3 | \$3244.80 | \$3374.59 | E |
Find the value of:
Calculate the total interest earned over the three years.
\$9000 is invested for three years at a rate of 5\% p.a. compounded annually.
Complete the table:
Calculate the total interest accumulated over three years.
Calculate the value of the investment at the end of the three years.
| Interest ($) | Balance ($) | |
|---|---|---|
| Starting balance | 0 | 9000 |
| After one year | ||
| After two years | ||
| After three years |
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:
| 5 \text{ years} | 10 \text{ years} | 15 \text{ years} | 20 \text{ years} | 25 \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.
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?
Find the future value of the following:
An investment of \$2000 earns interest at 6\% p.a, compounded annually over 4 years.
An investment of \$1000 earns interest at 2\% p.a., compounded semiannually over 3 years.
An investment of \$8030 earns interest at 3\% p.a., compounded annually over 20 years.
An investment of \$4490 earns interest at 2.8\% p.a., compounded semiannually over 6 years.
An investment of \$8030 earns interest at 3\% p.a., compounded quarterly over 12 years.
An investment of \$9450 earns interest at 2.6\% p.a., compounded monthly over 14 years.
An investment of \$1710 earns interest at 2.2\% p.a., compounded weekly over 6 years.
An investment of \$3000 earns interest at 4.5\% p.a., compounded daily over 5 years. Assume one leap year over this period.
An investment of \$392 earns interest at 2\% p.a., compounded annually for 7 years. After this time the principal plus interest is reinvested at 4\% p.a., compounded annually for 5 more years.
Maria has \$1000 to invest for 4 years and would like to know which of three investment plans to choose:
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.
Calculate the future value of each investment plan.
State which plan Maria should choose for maximum return on her investment.
Hannah put \$600 in a savings account with interest compounded quarterly at a rate of \\ 1.1\% p.a. Calculate the amount that is in Hannah's account after a period of 21 months.
Tina has \$900 in a savings account which earns compound interest at a rate of 2.4\% p.a.
If interest is compounded monthly, how much interest does Tina earn in 17 months?
John borrows \$6000 from a loan shark at a rate of 20\% p.a. compounded annually. If he is not able to make any repayments, calculate how much John will owe at the end of 5 years.
Emma borrows \$7000 from a loan shark at a rate of 4.7\% p.a. compounded annually. If she is not able to make any repayments, calculate how much Emma will owe at the end of 3 years.
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?
Tom wants to put a deposit on a house in 4 years time. In order to finance the \$12\,000 deposit, he decides to put some money into a high interest savings account that pays \\ 5\% p.a. interest, compounded monthly. If P is the amount of money that he must put into his account now to accumulate enough for the deposit, find P.
Ursula has just won \$30\,000. She decides to invest some of her winnings into a retirement fund which earns 8\% interest p.a., compounded yearly. When she retires in 29 years, she wants to have \$52\,000 in her fund.
How much of her winnings should Ursula invest now to achieve this?
Beth's investment into a 12-year 4.4\% p.a. corporate bond grew to \$13\,190.
Calculate the size of Beth's initial investment if the interest was compounded:
Annually
Semiannually
Quarterly
Monthly
Weekly
Daily
Victoria has been promised an inheritance of \$70\,000 in 5 years time. What is the most she can borrow now at a rate of 7\% p.a. compounded annually, and still be able to pay off the loan with her inheritance?