Skip to content

Mathematics and Statistics · Ch 18 — Commercial Mathematics

Simple Interest and Compound Interest

5

Simple Interest and Compound Interest

Interest is the price of money — what a borrower pays a lender for the use of a principal sum over time, at a stated rate.

Simple interest

On a principal PP at r%r\% per annum for nn years, simple interest (SI) is charged only on the original principal:

SI=P r n100,Amount=P+SI=P(1+rn100).\text{SI}=\frac{P\,r\,n}{100},\qquad \text{Amount}=P+\text{SI}=P\left(1+\frac{rn}{100}\right).

Compound interest

Under compound interest (CI) the interest earned each period is added to the principal, so the next period's interest is computed on the grown amount. Compounded annually,

Amount=P(1+r100)n,CI=Amount−P.\text{Amount}=P\left(1+\frac{r}{100}\right)^{n},\qquad \text{CI}=\text{Amount}-P.

SI grows linearly, CI grows faster

Note

Why CI exceeds SI (for n≥2n\ge2)

In year 1 both give the same interest. From year 2 onward, CI charges interest on the previous interest too ("interest on interest"), so it overtakes SI. For n=2n=2 years the gap is exactly

CI−SI=P(r100)2.\text{CI}-\text{SI}=P\left(\frac{r}{100}\right)^{2}.

Tip

More frequent compounding …

Definition 1Simple interest (SI)

SI=P r n100\text{SI}=\dfrac{P\,r\,n}{100}; interest on the original principal only. Amount $=P\left(1+\tfrac …

Definition 2Compound interest (CI)

Amount =P(1+r100)n=P\left(1+\tfrac{r}{100}\right)^{n} (annual compounding); CI=Amount−P\text{CI}=\text{Amount}-P. Each period's interest is a …

Definition 3CI–SI difference (2 years)

For n=2n=2 years, CI−SI=P(r100)2\text{CI}-\text{SI}=P\left(\dfrac{r}{100}\right)^{2} — a handy shortcut and a u …

Start your 14-day free trial to unlock the full solution →
← Previous · 4Commission and BrokerageNext · 6 →Shares and Dividends