Investments
Calculate simple and compound interest; find present and future values; interpret appreciation, inflation and depreciation; analyse shares, dividend yield and comparing investment options.
Worked examples
Simple vs compound interest
Straightforward
Problem
$5000 is invested for 3 years. Option A earns 6% per annum simple interest. Option B earns 5.8% per annum compound interest, compounded annually. Which option gives a higher final value?
1
Calculate the final value under Option A (simple interest).
2
Calculate the final value under Option B (compound interest).
3
Compare the two options.
Option A: $5900.00
Option B: $5922.32
Option B gives $22.32 more over 3 years.
Option B: $5922.32
Option B gives $22.32 more over 3 years.
Answer
Option B (compound at 5.8%) gives a higher final value of $5922.32, compared to $5900.00 for Option A (simple at 6%).
Present value and future value
Moderate
Problem
How much must be invested now at 5% per annum compound interest, compounded annually, to have $8000 in 4 years?
1
Write down the known values and the formula.
, ,
2
Calculate the denominator .
3
Divide to find the present value.
Answer
$6582.07 must be invested now.
Shares, dividend yield and total return
Challenging
Problem
An investor buys 200 shares at $8.40 each. After one year the share price is $9.10 and the company pays a dividend of $0.25 per share.
(a) Calculate the dividend yield at the time of purchase.
(b) Calculate the investor's total profit.
(a) Calculate the dividend yield at the time of purchase.
(b) Calculate the investor's total profit.
1
Calculate the dividend yield.
2
Calculate the capital gain.
3
Calculate the total dividends received.
4
Sum the capital gain and dividends for total profit.
Answer
(a) Dividend yield . (b) Total profit .
Practise
Q1·Straightforward
Mia invests $2000 at a simple interest rate of 4% per annum for 3 years. Calculate the interest earned using .
Explanation
Using the simple interest formula:
Q2·Straightforward
$1000 is invested at 5% per annum compound interest, compounded annually for 2 years. Find the final amount using .
Explanation
Using the compound interest formula:
Q3·Straightforward
Jordan invests $6000 at a simple interest rate of 3.5% per annum for 2 years. How much interest does he earn?
Explanation
Q4·Straightforward
$500 is invested at 6% per annum compound interest, compounded annually for 3 years. Find the final value of the investment, to the nearest cent.
Explanation
Q5·Moderate
How much must be invested today at 4% per annum compound interest (compounded annually) to have $5000 in 4 years? Give your answer to the nearest cent.
Explanation
Using the present value formula:
Q6·Moderate
$2000 is invested at 4% per annum interest, compounded quarterly, for 2 years. Find the final amount, to the nearest cent.
*(Hint: the quarterly rate is and there are compounding periods.)*
*(Hint: the quarterly rate is and there are compounding periods.)*
Explanation
Quarterly rate:
Number of periods:
Number of periods:
Q7·Moderate
A company's shares are priced at $12.50. The company pays an annual dividend of 50 cents per share. Calculate the dividend yield as a percentage.
Explanation
Q8·Moderate
A textbook costs $80 today. If inflation runs at 2.5% per annum, what will the same textbook cost in 3 years? Give your answer to the nearest cent.
Explanation
Q9·Moderate
An investor wants $10\,000 in 5 years. The investment earns 4% per annum compound interest, compounded annually. How much must they invest now? Give your answer to the nearest cent.
Explanation
Q10·Challenging
Sara has $3000 to invest for 4 years. Option A offers 5% per annum simple interest. Option B offers 4.8% per annum compound interest, compounded annually. How much more does the better option return? Give your answer to the nearest cent.
Explanation
**Option A (simple interest):**
**Option B (compound interest):**
**Difference:**
Option B (compound) returns $18.82 more.
**Option B (compound interest):**
**Difference:**
Option B (compound) returns $18.82 more.
Q11·Challenging
Tom buys 500 shares at $4.20 each. After one year the share price rises to $4.85 and the company pays a dividend of $0.16 per share. Calculate Tom's total profit (capital gain plus dividends).
Explanation
**Capital gain:**
**Dividends:**
**Total profit:**
**Dividends:**
**Total profit:**
Q12·Challenging
An investment of $4000 grows to $4630.50 over 3 years with compound interest, compounded annually. Find the annual interest rate as a percentage.
Explanation
**Verify:** ✓
Q13·Challenging
$2000 is invested at 5% per annum compound interest, compounded annually. After how many full years will the investment first exceed $2600? Use trial and error or successive calculation.
Explanation
Testing successive years:
| Year | Value |
|---|---|
| 5 | |
| 6 |
After 5 years: $2552.56 < $2600
After 6 years: $2680.19 > $2600
The investment first exceeds $2600 after **6 years**.
After 6 years: $2680.19 > $2600
The investment first exceeds $2600 after **6 years**.
Open Math
Investments
Financial Mathematics · MS-F4
Name:
Date:
Q1Straightforward
Mia invests $2000 at a simple interest rate of 4% per annum for 3 years. Calculate the interest earned using .
Q2Straightforward
$1000 is invested at 5% per annum compound interest, compounded annually for 2 years. Find the final amount using .
Q3Straightforward
Jordan invests $6000 at a simple interest rate of 3.5% per annum for 2 years. How much interest does he earn?
Q4Straightforward
$500 is invested at 6% per annum compound interest, compounded annually for 3 years. Find the final value of the investment, to the nearest cent.
Q5Moderate
How much must be invested today at 4% per annum compound interest (compounded annually) to have $5000 in 4 years? Give your answer to the nearest cent.
Q6Moderate
$2000 is invested at 4% per annum interest, compounded quarterly, for 2 years. Find the final amount, to the nearest cent.
*(Hint: the quarterly rate is and there are compounding periods.)*
*(Hint: the quarterly rate is and there are compounding periods.)*
Q7Moderate
A company's shares are priced at $12.50. The company pays an annual dividend of 50 cents per share. Calculate the dividend yield as a percentage.
Q8Moderate
A textbook costs $80 today. If inflation runs at 2.5% per annum, what will the same textbook cost in 3 years? Give your answer to the nearest cent.
Q9Moderate
An investor wants $10\,000 in 5 years. The investment earns 4% per annum compound interest, compounded annually. How much must they invest now? Give your answer to the nearest cent.
Q10Challenging
Sara has $3000 to invest for 4 years. Option A offers 5% per annum simple interest. Option B offers 4.8% per annum compound interest, compounded annually. How much more does the better option return? Give your answer to the nearest cent.
Q11Challenging
Tom buys 500 shares at $4.20 each. After one year the share price rises to $4.85 and the company pays a dividend of $0.16 per share. Calculate Tom's total profit (capital gain plus dividends).
Q12Challenging
An investment of $4000 grows to $4630.50 over 3 years with compound interest, compounded annually. Find the annual interest rate as a percentage.
Q13Challenging
$2000 is invested at 5% per annum compound interest, compounded annually. After how many full years will the investment first exceed $2600? Use trial and error or successive calculation.
Worked solutions and answers at openmath.au/year-12/standard-2/investments-and-loans/investments