Simple interest is calculated on the original principal each period. Compound interest is calculated on the current balance, including earlier interest. With principal P, annual simple rate r%, and t years, I= Prt100 and the amount is P+I. For compound interest at r% per period over n periods, A=P(1+ r100)n. Interest earned is A-P. This model assumes no extra deposits, withdrawals or fees. Example At 4% annually for 3 years, $2000 earns simple interest 2000(4)(3)100=$240, giving $2240. With annual compounding, A=2000(1.04)3=$2249.728, or $2249.73 to cents. Interest earned is $249.73. Match rate and period count. If a nominal annual rate of 4% is explicitly split into two half-yearly periods, use 2% each half-year and 6 periods for 3 years. Do not infer a compounding convention from missing wording.

Simple interest is calculated on the original principal each period. Compound interest is calculated on the current balance, including earlier interest. With principal $P$, annual simple rate $r\%$, and $t$ years, $I=\dfrac{Prt}{100}$ and the amount is $P+I$.

For compound interest at $r\%$ per period over $n$ periods, $A=P\left(1+\dfrac r{100}\right)^n$. Interest earned is $A-P$. This model assumes no extra deposits, withdrawals or fees.

At $4\%$ annually for $3$ years, $\$2000$ earns simple interest $\dfrac{2000(4)(3)}{100}=\$240$, giving $\$2240$.

With annual compounding, $A=2000(1.04)^3=\$2249.728$, or $\$2249.73$ to cents. Interest earned is $\$249.73$.

Match rate and period count. If a nominal annual rate of $4\%$ is explicitly split into two half-yearly periods, use $2\%$ each half-year and $6$ periods for $3$ years. Do not infer a compounding convention from missing wording.

Simple and compound interest

Simple and compound interest