Compound interest loans and investments

General Mathematics · Unit 4 — Investing and netw orking · Loans, investments and annuities 1

Learning objectives (4)

LO-1Calculate 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 LO-2Solve 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.LO-3Use a recurrence relation to model a compound interest loan or investment.  𝐴𝑛+1 = 𝑟𝐴𝑛 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, and 𝑟 = 1 + 𝑖 where 𝑖 is interest rate per compounding period LO-4Use the compound interest formula to model a compound interest loan or investment.  𝐴 = 𝑃(1 + 𝑖)𝑛 where 𝐴 is total amount, 𝑃 is principal, 𝑖 is interest rate per compounding period and 𝑛 is number of compounding periods

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