Simple interest

Q: What is the formula for simple interest?

SI = \dfrac{P \times R \times T}{100}, with P the principal, R the yearly rate in percent and T the time in years.

Q: How do you handle time given in months?

Convert it to years. 9 months is \tfrac{9}{12} = 0.75 years.

Interest is the extra money paid for borrowing or earned for saving. With simple interest, it is calculated on the original amount (the principal) only, so the same interest is added every year.

Formulas

Simple interest

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

Amount

A = P + S I

Finding the rate or the time

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

Worked examples

Example 1. Find the simple interest and amount on ₹5,000 at 8% per year for 3 years.

$S I = \frac{5000 \times 8 \times 3}{100} = 1200$ .
Amount = $5000 + 1200 = 6200$ .

Answer: SI ₹1,200, amount ₹6,200

Example 2. The simple interest on ₹6,000 for 2 years is ₹900. Find the rate per year.

$R = \frac{900 \times 100}{6000 \times 2} = \frac{90000}{12000}$ .
$R = 7.5$ .

Answer: 7.5% per year

Example 3. In how many years will ₹2,500 earn ₹375 at 6% per year?

$T = \frac{375 \times 100}{2500 \times 6} = \frac{37500}{15000}$ .
$T = 2.5$ .

Answer: 2.5 years

Common mistakes

Using months as years. If the time is given in months, divide by 12 first.
Forgetting to add the interest to the principal when the question asks for the amount.
Mixing up the rate and the time when substituting into the formula.

Practice questions with answers

1. Which formula gives the Simple Interest?

AS.I. = (P × R × T) / 100
BS.I. = (P × R × T) × 100
CS.I. = (P + R + T) / 100
DS.I. = (P × R) / T

Show answer

Answer: A) S.I. = (P × R × T) / 100

Simple Interest = (Principal × Rate × Time) / 100, where Rate is per cent per annum and Time is in years.

2. The simple interest on a certain sum for 3 years at 8% per annum is ₹180 more than the interest on the same sum for 2 years at 9% per annum.
Find the sum.

A6000
B3300
C3000
D2700

Show answer

Answer: C) 3000

Let

P

be the sum.

(P \times 8 \times 3) /100 - (P \times 9 \times 2) /100 = 180

→

(24 P - 18 P) /100 = 180

→

6 P /100 = 180

→

P = 18000/6

= ₹3000.

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Frequently asked questions

What is the formula for simple interest?

$S I = \frac{P \times R \times T}{100}$ , with $P$ the principal, $R$ the yearly rate in percent and $T$ the time in years.

What is the difference between interest and amount?

The interest is only the extra money. The amount is the principal plus the interest.

How is simple interest different from compound interest?

Simple interest is always on the original principal. Compound interest is on the principal plus the interest already earned, so it grows faster.

How do you handle time given in months?

Convert it to years. 9 months is $\frac{9}{12} = 0.75$ years.

Simple interest

Formulas

Worked examples

Common mistakes

Practice questions with answers

Practice by class

Frequently asked questions

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