Money and interest: Formulas

Foundation

Simple interest

S I = \frac{P \times R \times T}{100}

What each letter means
$S I$	the simple interest earned or paid (rupees)
$P$	the principal (the money first lent or deposited) (rupees)
$R$	the rate of interest, as a percent per year (percent per year)
$T$	the time (years)

Simple interest is a fixed percentage of the original money, paid every year, so it grows by the same amount each year.

Why it works

R% of P for one year is P × R / 100. For T years it is T times that: P × R × T / 100. The interest is always worked out on the original P, never on interest already earned (that would be compound interest).

When to use it

A loan or deposit where interest is charged only on the original amount, for a given rate per year and a number of years.

How to use it

Write P, R (as a number, not a percent sign) and T (in years).
Multiply P × R × T.
Divide by 100.
For the total amount, add SI to P.

To remember: PRT over 100.

Other forms

Same formula, another form $A = P + S I = P (1 + \frac{R T}{100})$ the total amount at the end
Rearranged $P = \frac{100 \times S I}{R \times T}$
Rearranged $R = \frac{100 \times S I}{P \times T}$
Rearranged $T = \frac{100 \times S I}{P \times R}$

Worked examples

Story

Riya deposits ₹12,000 in a bank at 6.5% simple interest per year for 2 years. How much interest does she earn, and how much does she get back?

$S I = \frac{12000 \times 6.5 \times 2}{100} = 1560$
Amount = 12000 + 1560 = ₹13,560

Answer: 1560

Picture

Plot the interest on ₹1,000 at 10% per year after 1, 2, 3 and 4 years. What shape does the graph make?

Each year the interest grows by 1000 × 10 / 100 = ₹100.
Points: (1, 100), (2, 200), (3, 300), (4, 400).
They lie on a straight line through (0, 0).

Answer: A straight line through the origin: ₹100 more each year

Direct

Find the simple interest on ₹5,000 at 8% per year for 3 years.

$S I = \frac{5000 \times 8 \times 3}{100}$
$= \frac{120000}{100} = 1200$

Answer: 1200

Reverse

At what rate of simple interest will ₹4,000 earn ₹960 in 3 years?

Try it first, then show the working

$R = \frac{100 \times S I}{P \times T}$
$= \frac{100 \times 960}{4000 \times 3} = \frac{96000}{12000}$
R = 8% per year

Answer: 8

Exam

A sum of money doubles itself in 8 years at simple interest. Find the rate.

Try it first, then show the working

If it doubles, the interest equals the principal: SI = P.
$P = \frac{P \times R \times 8}{100}$
$1 = \frac{8 R}{100} \Rightarrow R = 12.5$
The rate is 12.5% per year.

Answer: 12.5

Common mistake: Using months as years (6 months is T = 0.5), or putting R in as 0.08 and still dividing by 100.