General Mathematics · Unit 4 · Loans, investments and annuities 1 · Compound interest loans and investments

Calculate the effective annual rate of interest, 𝑖effective, and use the results to compare interest on loans or investments when interest is paid or charged for different compounding periods, including daily, monthly, quarterly and six-monthly.  𝑖effective = (1 + 𝑖)𝑘 − 1 where 𝑖 is interest rate per compounding period and 𝑘 is number of compounding periods per year

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Question 1

An investment account earns interest at a rate of 6.2% per annum, compounded quarterly. (a) Calculate the interest rate per quarter. (1 mark) (b) Use your result from part (a) to calculate the effective annual rate of interest as a percentage, correct to 2 decimal places. (2 marks)

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Question 2

An investment account offers an annual interest rate of 6.8% per annum, compounded six-monthly. Calculate the effective annual rate of interest as a percentage, correct to two decimal places.

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Question 3

An investment earns interest daily at $4.38\%$ per annum. What is the effective annual rate of interest, correct to two decimal places?

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Question 4

Three banks offer different interest rates and compounding periods for a \$15{,}000 investment over one year. The table below shows the advertised annual interest rate and compounding frequency for each bank. (a) Calculate the effective annual rate of interest for each bank. Express your answers as percentages correct to two decimal places. (3 marks) (b) Determine which bank offers the best return for the investment and justify your answer. (1 mark)

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Question 5

An investment account offers an annual interest rate of 6.8% compounded fortnightly (every two weeks). Calculate the effective annual rate of interest as a percentage, correct to two decimal places.

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Question 6

An investment account offers an annual interest rate of 4.8% compounded fortnightly. Which of the following is closest to the effective annual rate of interest?

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More in Compound interest loans and investments

Solve practical problems involving compound interest loans or investments, including determining the total amount of the loan or investment, total interest, principal, interest rate per year and per compounding period, and the effect of the interest rate and number of compounding periods on the total amount.

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