Simple Interest

Just as you pay rent to use a car, you pay “rent” for using someone’s money — that is interest. The money borrowed is the principal ( $P$ ), the yearly rent rate the rate of interest ( $R %$ ), the period for which it is kept the time ( $T$ ), and the total returned the amount ( $A$ ). In simple interest the interest is charged each year only on the original sum, so it is the same every year.

S I = \frac{P \times R \times T}{100}, A = P + S I = P (1 + \frac{R T}{100})

The two core formulas

$P$: principal
$R$: rate per annum (%)
$T$: time (in years)
$A$: amount

1

The formula and its four forms

Finding any one of

S I

,

P

,

R

,

T

Given three of the four quantities, finding the fourth.

Interest, principal, rate, time

Turning the formula around

The formula for each variable and solved examples.

To find	Formula
SI	$\frac{P R T}{100}$
P	$\frac{S I \times 100}{R T} या \frac{A \times 100}{100 + R T}$
R	$\frac{S I \times 100}{P T}$
T	$\frac{S I \times 100}{P R}$

Example 1 · Basic

Find the simple interest and the amount on ₹7,500 at 8% per annum for 3 years.

Solution, step by step

1 $S I = \frac{7500 \times 8 \times 3}{100} = 1800$ .
2Amount $= 7500 + 1800 = 9300$

Answer ₹1,800 and ₹9,300

Example 2 · Standard

A sum amounts to ₹7,200 in 4 years at 5% simple interest per annum. What was the sum?

Solution, step by step

1 $A = P (1 + \frac{5 \times 4}{100}) = 1.2 P$ .
2 $P = \frac{7200}{1.2} = 6000$

Answer ₹6,000

Example 3 · Standard

₹4,000 earned ₹960 simple interest in 3 years. What is the rate per annum?

Solution, step by step

1 $R = \frac{960 \times 100}{4000 \times 3}$ .
2 $= 8%$

Answer 8%

Example 4 · Advanced

Part of ₹15,000 is lent at 6% and the rest at 8% per annum, and the total interest in 1 year is ₹1,060. How much is at 8%?

Solution, step by step

1If all were at 6% the interest would be $900$ . The gap is $1060 - 900 = 160$ .
2Each rupee at 8% adds 2% extra ⟹ the 8% part $= \frac{160}{0.02} = 8000$ .

Answer ₹8,000

BasicTry it yourself first

What is the simple interest on ₹3,000 at 6% per annum for 4 years?

BasicTry it yourself first

What is the simple interest on ₹5,600 at 5% per annum for 2 years?

StandardTry it yourself first

What is the simple interest on ₹12,500 at 7.5% per annum for 3 years?

BasicTry it yourself first

₹2,000 is lent at 10% simple interest per annum for 3 years. What is the amount?

StandardTry it yourself first

₹8,400 is lent at 6.5% simple interest per annum for 5 years. What is the amount?

BasicTry it yourself first

A sum at 10% simple interest per annum amounts to ₹5,600 in 4 years. What was the principal?

StandardTry it yourself first

A sum at 6% simple interest per annum amounts to ₹13,000 in 5 years. What was the principal?

AdvancedTry it yourself first

A sum at 7.5% simple interest per annum amounts to ₹15,600 in 4 years. What was the principal?

BasicTry it yourself first

₹2,000 earns ₹400 simple interest in 4 years. What is the rate per annum?

StandardTry it yourself first

₹7,500 earns ₹1,350 simple interest in 3 years. What is the rate per annum?

AdvancedTry it yourself first

₹16,000 earns ₹3,520 simple interest in 2.5 years. What is the rate per annum?

BasicTry it yourself first

In how many years will ₹4,000 become ₹5,200 at 10% simple interest per annum?

StandardTry it yourself first

In how many years will ₹6,500 become ₹8,255 at 7.5% simple interest per annum?

AdvancedTry it yourself first

In how many years will ₹9,000 become ₹11,340 at 4% simple interest per annum?

Units of time

Days · months · half-years · quarters

If the rate is yearly, convert the time to years; if it is half-yearly or quarterly, convert it to a yearly rate.

Time	In years
1 month	$\frac{1}{12}$
3 months	$\frac{1}{4}$
9 months	$\frac{3}{4}$
73 days	$\frac{73}{365} = \frac{1}{5}$
146 days	$\frac{2}{5}$

RememberA half-yearly rate means that much interest every 6 months; the yearly rate is double. For a quarterly rate it is four times. In simple interest there is no interest on interest, so simply converting to a yearly rate works.

When counting days, the day the money is deposited is not counted but the day it is withdrawn is. Usually 1 year = 365 days.

Example 5 · Standard

What is the simple interest on ₹14,600 at 10% per annum for 146 days?

Solution, step by step

1 $T = \frac{146}{365} = \frac{2}{5}$ year.
2 $S I = 14600 \times \frac{10}{100} \times \frac{2}{5} = 584$

Answer ₹584

Example 6 · Standard

Find the simple interest on ₹6,000 at 3% half-yearly for 2 years.

Solution, step by step

1Annual rate $= 3 \times 2 = 6%$ .
2 $S I = \frac{6000 \times 6 \times 2}{100} = 720$

Answer ₹720

Example 7 · Standard

In what time will ₹8,000 become ₹9,080 at 4.5% simple interest per annum?

Solution, step by step

1Interest $= 9080 - 8000 = 1080$ .
2 $T = \frac{1080 \times 100}{8000 \times 4.5} = 3$ years

Answer 3 years

BasicTry it yourself first

What is the simple interest on ₹10,000 at 6% per annum for 73 days? (1 year = 365 days)

StandardTry it yourself first

What is the simple interest on ₹18,250 at 6% per annum for 146 days? (1 year = 365 days)

AdvancedTry it yourself first

What is the simple interest on ₹21,900 at 5% per annum for 219 days? (1 year = 365 days)

BasicTry it yourself first

What is the total simple interest on ₹5,000 at 2% half-yearly for 3 years?

StandardTry it yourself first

What is the total simple interest on ₹8,000 at 1.5% quarterly for 2 years?

StandardTry it yourself first

What is the total simple interest on ₹12,000 at 4% half-yearly for 2.5 years?

AdvancedTry it yourself first

What is the total simple interest on ₹15,000 at 2.5% quarterly for 3 years?

StandardTry it yourself first

A man borrows ₹20,000 at 6% per annum and lends the same sum at 8.5%. What is his gain in 3 years?

AdvancedTry it yourself first

A man borrows ₹36,000 at 7.25% per annum and lends the same sum at 9%. What is his gain in 4 years?

2

$n$ times, two sums and two amounts

Interest from multiples of the principal

How many times the sum grows, how much interest and how long; and finding the principal from two amounts.

A sum becoming $n$ times

Interest

= (n - 1) \times

principal

Rate-time relations when a sum doubles, triples, and so on.

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Two sums, two amounts

Take the difference

The gain from borrowing and lending, the difference of two rates, a split sum and two amounts.

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3

Payment by instalments

Interest on the time each instalment stays unpaid

Comparing a cash price with an instalment scheme; the value of equal instalments.

Equal monthly instalments

No interest on the last instalment

Each instalment carries interest for the months it stays unpaid.

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4

Traps and fast tricks

Slips · tricks

Where marks are lost in simple interest.

The commonest mistakes

Six traps

The slips that cost marks.

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Fast tricks

Multipliers and ratios

Tricks that shorten the work.

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5

The practice ladder

Basic → standard → advanced

New questions of every type, in three levels.

Level 1 — Basic

Direct rules

One-rule questions.

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Level 2 — Standard

Two ideas combined

Exam-level questions.

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Level 3 — Advanced

Many steps and clever thinking

Questions at the hard end of competitive exams.

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6

Revision — formula cards

Flip each card and test yourself

Read the front, think, then flip.

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The formula and its four forms

Interest, principal, rate, time

Units of time

$n$ times, two sums and two amounts

A sum becoming $n$ times

Two sums, two amounts

Payment by instalments

Equal monthly instalments

Traps and fast tricks

The commonest mistakes

Fast tricks

The practice ladder

Level 1 — Basic

Level 2 — Standard

Level 3 — Advanced

Revision — formula cards

Free All Access Passevery mind map · Hindi + English · 12 months

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