SSC CGL Maths · Simple and Compound Interest

Interest as a Fraction of the Sum

The interest as a percent of the principal is the rate times the years, so a question that never names the sum can still be solved.

All Simple and Compound Interest notes

Why this matters

Twenty-one questions in the bank, nineteen of them EASY: the interest is three-fifths of the sum, the sum becomes 8/7 of itself, a sum triples in 16 years, or the interest for new years and rates is wanted. One fact, rate times years, answers all of them in a line.

Concept 1 of 3: Simple interest as a fraction of the principal

Divide the simple interest formula by the principal and the principal disappears. What is left says that rate times years is the interest as a percent of the sum, whatever the sum is.

Definition

$\frac{SI}{P} = \frac{R \times T}{100}$ . So the interest is $(R \times T)\%$ of the principal.
Interest given as a fraction $\frac{a}{b}$ of the sum in $T$ years: $R = \frac{100}{T} \times \frac{a}{b}$ .
Amount given as a fraction of the sum: subtract 1 first. Becoming $\frac{7}{4}$ of itself means the interest is $\frac{3}{4}$ of it.
Interest a fixed number of rupees less than the sum: if the interest is $k$ times the sum, then $P - kP$ equals that number of rupees.
Fast route: turn the fraction into a percent, then divide by the years. Three-fifths is 60%; over 12 years that is 5% a year.

Interest as a share of the principal

\frac{SI}{P} = \frac{R \times T}{100} \qquad R = \frac{100}{T} \times \frac{SI}{P}

Worked example

The simple interest on a sum for 5 years is two-fifths of the sum. Find the rate.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 25 Sep 2024, Shift 1 · Q63Easy

Example 1 · Simple and Compound Interest · Interest as a Fraction of the Sum

The simple interest on a sum for 6 years is three-fifth of the sum. The rate of interest per annum is:

Reading the amount's fraction as the interest's fraction

A sum that becomes

\frac{8}{7}

of itself has earned

\frac{1}{7}

of itself, not

\frac{8}{7}

. The amount includes the sum; take 1 away before you find the rate.

Drill 8 more on simple interest as a fraction of the principal

Concept 2 of 3: A sum that becomes n times itself at simple interest

To become n times itself the sum must earn n minus 1 copies of itself. Under simple interest every copy takes the same number of years, so the time grows with n minus 1, not with n.

Definition

Becoming $n$ times means $SI = (n - 1)P$ , so $R \times T = 100(n - 1)$ .
Doubling: $R \times T = 100$ . Tripling: $R \times T = 200$ .
Same rate, a new multiple: the times are in the ratio of $n - 1$ : $T_2 = T_1 \times \frac{n_2 - 1}{n_1 - 1}$ .
Fast route: a sum that doubles in 7 years earns one copy in 7 years, so four times (three copies) takes 21 years.

Becoming n times at simple interest

R \times T = 100(n - 1) \qquad T_2 = T_1 \times \frac{n_2 - 1}{n_1 - 1}

nhow many times its own value the sum becomes
$T_1, T_2$ the times taken to become $n_1$ and $n_2$ times

Worked example

A sum doubles in 10 years at simple interest. Find the rate, and the years it takes to become 4 times itself.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 19 Sep 2025, Shift 3 · Q57Easy

Example 2 · Simple and Compound Interest · Interest as a Fraction of the Sum

A sum becomes 2.5 times of itself in 5 years under simple interest. In how many years will it become 5 times itself at the same rate?

Scaling the time by n instead of n minus 1

A sum that doubles in 5 years at simple interest does not become 4 times in 10 years. Doubling is one copy of interest; four times is three copies, so it takes 15 years.

Drill 6 more on a sum that becomes n times itself at simple interest

Concept 3 of 3: Simple interest scales with principal, rate and time

Double the sum, the rate or the years and the interest doubles. So a known interest under one set of terms gives the interest under any other terms by a ratio.

Definition

$SI$ is proportional to each of $P$ , $R$ and $T$ .
Same sum and rate: interests are in the ratio of the times. Same sum: interests are in the ratio of rate times time.
New terms on a known interest: $SI_2 = SI_1 \times \frac{R_2 T_2}{R_1 T_1}$ for the same sum.
Interest on the interest: if $B$ is the interest on $A$ , and $C$ is the interest on $B$ for the same rate and time, then $\frac{B}{A} = \frac{C}{B}$ , so $B^2 = AC$ .
Comparing two deals on one sum: compare rate times time. 7% for 2 years (14%) earns less than 5% for 3 years (15%).

Scaling simple interest

\frac{SI_2}{SI_1} = \frac{P_2 R_2 T_2}{P_1 R_1 T_1} \qquad B^2 = AC

$A, B, C$ a sum, its interest, and the interest on that interest, all at one rate and time

Worked example

The simple interest on a sum for 3 years at 6% per annum is ₹540. Find the simple interest on the same sum for 5 years at 8% per annum.

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 26 Sep 2025, Shift 2 · Q52Easy

Example 3 · Simple and Compound Interest · Interest as a Fraction of the Sum

If the simple interest on a certain sum of money for 4 years at

5\%

per annum is ₹500, what would be the simple interest on the same sum for 6 years at

7\%

per annum?

Comparing the rates alone

The higher rate does not always earn more. On the same sum, 9% for 2 years (18%) earns less than 4% for 5 years (20%): compare rate times time.

Drill 4 more on simple interest scales with principal, rate and time

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 as a fraction of the principal
Interest as a share of the principal
$\frac{SI}{P} = \frac{R \times T}{100} \qquad R = \frac{100}{T} \times \frac{SI}{P}$
A sum that becomes n times itself at simple interest
Becoming n times at simple interest
$R \times T = 100(n - 1) \qquad T_2 = T_1 \times \frac{n_2 - 1}{n_1 - 1}$
Simple interest scales with principal, rate and time
Scaling simple interest
$\frac{SI_2}{SI_1} = \frac{P_2 R_2 T_2}{P_1 R_1 T_1} \qquad B^2 = AC$

Watch out for (3)

Reading the amount's fraction as the interest's fraction
→ Simple interest as a fraction of the principal
Scaling the time by n instead of n minus 1
→ A sum that becomes n times itself at simple interest
Comparing the rates alone
→ Simple interest scales with principal, rate and time

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 21 questions