SSC CGL Maths · Simple and Compound Interest

Simple Interest

Simple interest is paid on the original sum only, so every year earns the same interest: the rate percent of the principal.

All Simple and Compound Interest notes

Why this matters

Fifteen questions in the bank, thirteen EASY and two MODERATE, five from each year: find the interest or the amount, count months and days, or work back from the amount to the principal. These are the marks to take in under 30 seconds, so learn the one-line routes.

Concept 1 of 3: Simple interest formula and the amount

The lender charges the same fee every year, worked out on the money first lent. Three years cost three times one year. Nothing is ever charged on the interest itself.

Definition

Principal $P$ : the sum lent or invested. Rate $R$ : the percent charged each year. Time $T$ : in years.
Simple interest: $SI = \frac{P \times R \times T}{100}$ . Amount: $A = P + SI$ , the total paid back.
Fast route: multiply the rate by the years first. At 8% for 3 years the interest is 24% of the principal, so you take one percentage, not three.
Use fractions for friendly rates: 12.5% is $\frac{1}{8}$ , 20% is $\frac{1}{5}$ , 25% is $\frac{1}{4}$ .
Earn at one rate, pay at another (a bank, a fee): the gain is the difference of the two rates on the same sum.

Simple interest and amount

SI = \frac{P \times R \times T}{100} \qquad A = P + SI = P\left(1 + \frac{R T}{100}\right)

Pprincipal, the sum lent
Rrate percent per year
Ttime in years
Aamount, principal plus interest

Worked example

Find the simple interest and the amount on ₹4,500 at 8% per annum for 3 years.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 18 Sep 2025, Shift 3 · Q58Easy

Example 1 · Simple and Compound Interest · Simple Interest

An educational fund of ₹6,00,000 earns simple interest at

9\%

per annum. This annual interest is used to grant three scholarships. If the first and third scholarships are ₹18,000 and ₹22,000 respectively, what is the value of the second scholarship?

Giving the amount when the interest is asked

The options usually print both the interest and the amount. Read the last line of the question again: interest is what is earned, the amount is principal plus interest.

Taking a percentage earning on the interest

A percentage earning or return is always a percent of the sum invested. If ₹50,000 earns a net ₹4,000 after a fee, the earning is

\frac{4000}{50000} = 8\%

, a percent of the sum and not of the interest.

Drill 5 more on simple interest formula and the amount

Concept 2 of 3: Simple interest for months and days

The rate is per year, so the time must be in years too. Six months is half a year and earns half a year's interest.

Definition

Months: $T = \frac{\text{months}}{12}$ . 9 months is $\frac{3}{4}$ year; 21 months is $1\frac{3}{4}$ years.
Dates on the same day of the month (10 March to 10 September): count whole months.
Days: $T = \frac{\text{days}}{365}$ . Do not count the day the money is lent; do count the day it is repaid. February has 29 days in a leap year (2012, 2016, 2020, 2024), and the bank's key then divides by 366.
Fast route: a 12% yearly rate is 1% a month. 18% a year is 1.5% a month.

Time in years

T = \frac{\text{months}}{12} \qquad T = \frac{\text{days}}{365}

Worked example

Find the simple interest on ₹9,000 at 10% per annum for 9 months.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 19 Sep 2025, Shift 1 · Q57Easy

Example 2 · Simple and Compound Interest · Simple Interest

Sarah lent ₹12000 to John on 10 January 2024 at a simple interest rate of

6\%

per annum. John plans to pay back the entire amount on 10 July 2024. What is the total amount John needs to return?

Putting months in place of years

SI = \frac{P \times R \times 8}{100}

for 8 months charges 8 years of interest. Divide the months by 12 first: 8 months is

\frac{2}{3}

year.

Counting both the first and the last day

Money lent on 24 January earns from 25 January. Count the days left in the first month without the start date, then the full months, then the days of the last month up to the repayment date.

Drill 5 more on simple interest for months and days

Concept 3 of 3: Principal from the amount (present worth)

If a sum grows to an amount by gaining a fixed share of itself, you get back to the sum by dividing that share out, not by taking a percent off the amount.

Definition

The amount is the principal times one growth factor: $A = P\left(1 + \frac{RT}{100}\right)$ . So $P = \frac{100A}{100 + RT}$ .
Present worth of a sum due later is the principal that grows to it by that date. It is found the same way.
Settling a debt early: find the debt's present worth today, then let it grow at the same rate to the day you pay. SSC's keys use this method.
Fast route: at 9.5% for 2 years the factor is 1.19, so $P = A \div 1.19$ . Check by growing $P$ back.

Principal from amount

P = \frac{100 \times A}{100 + R T}

Athe amount, or the sum due later
Pthe principal, or the present worth

Worked example

What principal amounts to ₹5,900 in 3 years at 6% per annum simple interest?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 26 Sep 2024, Shift 2 · Q60Easy

Example 3 · Simple and Compound Interest · Simple Interest

What principal would amount to ₹21,420 in 2 years at the rate of

9.5\%

p.a. simple interest?

Taking the percent off the amount

At 19% for the period, the principal is the amount divided by 1.19, not 81% of the amount. 81% of ₹11,900 is ₹9,639, but the principal is ₹10,000.

Drill 2 more on principal from the amount (present worth)

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (3)

Simple interest formula and the amount
Simple interest and amount
$SI = \frac{P \times R \times T}{100} \qquad A = P + SI = P\left(1 + \frac{R T}{100}\right)$
Simple interest for months and days
Time in years
$T = \frac{\text{months}}{12} \qquad T = \frac{\text{days}}{365}$
Principal from the amount (present worth)
Principal from amount
$P = \frac{100 \times A}{100 + R T}$

Watch out for (5)

Giving the amount when the interest is asked
→ Simple interest formula and the amount
Taking a percentage earning on the interest
→ Simple interest formula and the amount
Putting months in place of years
→ Simple interest for months and days
Counting both the first and the last day
→ Simple interest for months and days
Taking the percent off the amount
→ Principal from the amount (present worth)

Test yourself on Simple and Compound Interest

20 past SSC CGL questions from this chapter, timed at 12 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

Take the Simple and Compound Interest chapter test Drill all 15 questions