Perpetuities and future value of ordinary annuities

General Mathematics · Unit 4 — Investing and netw orking · Loans, investments and annuities 2

Learning objectives (5)

LO-1Solve practical problems involving perpetuities, including determining the total amount of the perpetuity, periodic payment and interest rate per compounding period. General Mathematics 2025 v1.3 LO-2Solve practical problems involving the future value of an ordinary annuity, including determining the total amount of the annuity, periodic payment, total payments and total interest.LO-3Use 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 LO-4Use 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 LO-5Use 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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