SL 1.4—Financial applications

For a fixed principal P and periodic rate i, simple interest grows linearly: A = P(1 + in). Compound interest grows by repeatedly multiplying the current balance: A = P(1 + i)ⁿ. Here i must be the rate per compounding period and n the number of those periods.

At 5% nominal annual interest compounded quarterly, the periodic rate is 0.05/4 and two years contains eight periods. A $1000 balance is therefore 1000(1 + 0.05/4)⁸, not 1000(1.05)².

Match the rate and number of periods before calculating. A quoted annual rate may be nominal or effective; deposits or withdrawals at different times require an annuity model rather than the one-payment formula.

Annual depreciation at rate $r$ uses $V_n=P(1-r)^n$. Inflation changes real value: if a nominal investment grows by factor $1+i$ while prices grow by $1+j$, its real-value factor per year is $(1+i)/(1+j)$. Always convert a nominal annual rate to the matching yearly, half-yearly, quarterly or monthly period before using technology or a financial package.