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Finance maths

Simple interest

Interest paid only on the original amount, so it grows by the same sum every year.

I=Prt
Total amountA=P(1+rt)

Calculator

The live calculator needs JavaScript. The worked example below shows the same steps it would.

See it move

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  • After 20 years: simple interest 2,000.00 (dashed), yearly compounding 2,653.30 (steps), continuous 2,718.28 (smooth curve).
  • Compound growth doubles the money roughly every 14.2 years.

What the symbols mean

I
the interest earned (or owed)
P
the principal: the amount invested or borrowed
r
the annual interest rate as a decimal (5% = 0.05; the calculator accepts 5%)
t
the time in years (years)

When to use it

Use it when interest is calculated on the starting amount only and is not added back to earn more interest: some short-term loans, bonds paying fixed coupons, and many textbook problems. If the interest is added to the balance each period, use compound interest instead.

Worked example

1,000 is invested at 5% simple interest for 3 years. How much interest does it earn?

  1. Start from the formula.

    I=P⁢r⁢t

  2. Substitute P = 1,000.00, r = 0.05, t = 3 and work it out.

    I=1,000.00·0.05·3
    =50.00·3
    =150.00

  3. The total at the end is the principal plus the interest:

    A=P+I
    =1,000.00+150.00
    =1,150.00

Answer I = 150, so the total is 1,150

Why it works

Each year the interest is the same fraction r of the same principal P, so after t years it is t lots of Pr.

Common mistakes

  • Using 5 instead of 0.05 for the rate, which makes the interest 100 times too big.
  • Mixing months and years: 18 months is t = 1.5, not 18.
  • Applying simple interest to a savings account that compounds; it underestimates the growth.