Investments and loans

Apply simple and compound interest to investments and loans; calculate present and future values; analyse shares, dividends and reducing-balance loans.

Financial Mathematics · MS-F4

Sub-topics

Investments

Calculate simple and compound interest; find present and future values; interpret appreciation, inflation and depreciation; analyse shares, dividend yield and comparing investment options.

Reducing-balance loans

Model reducing-balance loans using a recurrence relation; track repayments and interest using a table; compare loan options; analyse credit cards and interest-free periods.

Open Math

Investments and loans

Financial Mathematics · MS-F4

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Investments

Q1Straightforward

Mia invests $2000 at a simple interest rate of 4% per annum for 3 years. Calculate the interest earned using

I = Prt

Q2Straightforward

$1000 is invested at 5% per annum compound interest, compounded annually for 2 years. Find the final amount

A

using

A = P(1 + r)^n

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

\frac{4\%}{4} = 1\%

and there are

2 \times 4 = 8

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.

Reducing-balance loans

Q14Straightforward

A loan has an opening balance of $20\,000. The monthly interest rate is 0.5% and the monthly repayment is $500. Find the closing balance at the end of month 1.

Q15Straightforward

A loan has an opening balance of $8000. The monthly interest rate is 0.6%. Calculate the interest charged in the first month.

Q16Straightforward

A credit card has an outstanding balance of $1500. Interest is charged at 18% per annum, compounded monthly. No repayment is made. What is the balance at the end of one month?

Q17Moderate

A loan has an opening balance of $10\,000. The monthly interest rate is 0.5% and the monthly repayment is $450. Find the closing balance at the end of month 2.

Q18Moderate

A loan is modelled by the recurrence relation

A_{n+1} = 1.005 \times A_n - 300

with

A_0 = \$8000

. Find the closing balance at the end of month 3, to the nearest cent.

Q19Moderate

A loan has an opening balance of $20\,000. The monthly interest rate is 0.5% and the monthly repayment is $800. Find the closing balance at the end of month 3, to the nearest cent.

Q20Moderate

A credit card purchase of $800 has an interest-free period that has now ended. Interest is then charged at 22% per annum, compounded monthly, with no repayment made. Find the outstanding balance after 2 months of interest charges, to the nearest cent.

Q21Moderate

Two loans each have an opening balance of $15\,000. Loan A charges 6% per annum (compounded monthly); Loan B charges 5.4% per annum (compounded monthly). Both charge monthly repayments of $400. How much more interest does Loan A charge in the first month compared to Loan B?

Q22Challenging

A home loan has an opening balance of $25\,000. The monthly interest rate is 0.75% and the monthly repayment is $1000. Find the closing balance at the end of month 3, to the nearest cent.

Q23Challenging

A loan has an opening balance of $3000. The monthly interest rate is 1% and the monthly repayment is $300. After how many months is the loan fully repaid? (The final payment may be less than $300.)

Q24Challenging

A personal loan has an opening balance of $5000. The monthly interest rate is 1% and the monthly repayment is $500. Calculate the total interest paid over the life of the loan, to the nearest cent.

Q25Challenging

A credit card has an outstanding balance of $2000. Interest is charged at 18% per annum, compounded monthly. Only the minimum repayment of $50 per month is made. Find the outstanding balance at the end of month 3, to the nearest cent.

Worked solutions and answers at openmath.au/year-12/standard-2/investments-and-loans