General Mathematics · Unit 4 · Loans, investments and annuities 2 · Perpetuities and future value of ordinary annuities

Use the future value annuity formula to model the future value of an ordinary annuity, e.g. compound interest investment with periodic payments where interest is calculated before the periodic payment is made.  𝐴𝐹𝑉 = 𝑑 ((1+𝑖)𝑛−1 𝑖) where 𝐴𝐹𝑉 is total amount, 𝑑 is periodic payment, 𝑖 is interest rate per compounding period and 𝑛 is number of compounding periods

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Question 1

Priya deposits $\$350$ at the end of each quarter into a savings account earning $2.8\%$ per annum, compounded quarterly. Calculate the total value of her annuity after 5 years, to the nearest cent.

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Question 2

Calculate the balance of this annuity at the end of the third quarter.

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Question 3

Sarah deposits $350 at the end of each quarter into a savings account earning 5.2% per annum compounded quarterly. Calculate the value of the annuity after 5 years, to the nearest dollar.

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Question 4

Jo contributes $350 at the end of each month to an annuity earning 5.4% p.a. compounding monthly. (a) Determine the value of i and n for a 5-year investment period. (1 mark) (b) Calculate the future value of Jo's annuity at the end of 5 years, to the nearest dollar. (2 marks) (c) Determine the total interest earned over the 5-year period, to the nearest dollar. (1 mark)

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Question 5

Every quarter, Maya deposits $\$1{,}200$ into a savings account that earns $5.2\%$ per annum, compounding quarterly. Calculate the value of the annuity at the end of 5 years, to the nearest dollar.

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More in Perpetuities and future value of ordinary annuities

Use a recurrence relation to model the future value of an ordinary annuity, e.g. compound interest investment with periodic payments where interest is calculated before the periodic payment is made.  𝐴𝑛+1 = 𝑟𝐴𝑛 + 𝑑 where 𝐴𝑛+1 is total amount at the beginning of the (𝑛 + 1)th period, 𝐴𝑛 is total amount at the beginning of the 𝑛th period, 𝑑 is periodic payment and 𝑟 = 1 + 𝑖 where 𝑖 is interest rate per compounding period

Use the perpetuity formula, 𝐴 = 𝑑 𝑖 where 𝐴 is total amount, 𝑑 is periodic payment and 𝑖 is interest rate per compounding period.

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