SSC CGL Maths · Simple and Compound Interest

Finding the Rate, Time or Principal

The simple interest formula links four numbers, so any three of them give the fourth: the rate, the time or the principal.

All Simple and Compound Interest notes

Why this matters

Twenty-eight questions in the bank, the largest page in the chapter, and twenty-five of them are EASY. Most give a sum and an amount and ask for the rate or the years; the rest give two amounts at two times, two equal interests, or a rate tied to the time. Find one year's interest first and most of them take one division.

Concept 1 of 4: Finding the rate or the time from the interest

One year's interest is a fixed slice of the principal. Once you know the slice, the number of slices in the total interest is the time, and the slice as a percent of the principal is the rate.

Definition

First get the interest: $SI = A - P$ .
Rate: $R = \frac{100 \times SI}{P \times T}$ . Time: $T = \frac{100 \times SI}{P \times R}$ . Principal: $P = \frac{100 \times SI}{R \times T}$ .
Fast route for time: one year's interest is $R\%$ of $P$ ; time $=$ total interest $\div$ one year's interest.
Same rate, new sum: find the rate from the first deal, then use it on the second sum and time.
When the options differ only in a fraction, divide exactly and leave the answer as a mixed number. Do not round.

Rate, time and principal

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

Worked example

In how many years will ₹6,000 amount to ₹7,260 at 7% per annum simple interest?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 19 Sep 2025, Shift 2 · Q58Easy

Example 1 · Simple and Compound Interest · Finding the Rate, Time or Principal

At what rate of simple interest will ₹2,000 become ₹2,520 in 4 years?

Using the amount as the interest

When a question says a sum becomes or amounts to a figure, that figure includes the principal. Subtract the principal before you divide, or the rate comes out far too large.

Rounding the rate too early

SSC prints rate options that share a whole number and differ only in the fraction, such as

10\frac{2}{63}\%

10\frac{5}{63}\%

10\frac{10}{63}\%

and

10\frac{13}{63}\%

. Keep the fraction exact to the end; a rounded decimal cannot pick between them.

Drill 15 more on finding the rate or the time from the interest

Concept 2 of 4: Two amounts after two different times

Under simple interest the amount climbs by the same step every year. Two amounts at two times show you the step, and stepping back to year 0 gives the principal.

Definition

Interest per year $= \frac{A_2 - A_1}{t_2 - t_1}$ , the rise divided by the gap in years.
Principal $= A_1 - t_1 \times$ interest per year.
Rate $= \frac{\text{interest per year}}{P} \times 100$ .
Fast route for the principal: $P = \frac{t_2 A_1 - t_1 A_2}{t_2 - t_1}$ , one line with no rate needed.

Two amounts at two times

\text{Interest per year} = \frac{A_2 - A_1}{t_2 - t_1} \qquad P = \frac{t_2 A_1 - t_1 A_2}{t_2 - t_1}

$A_1, A_2$ the amounts after $t_1$ and $t_2$ years
$t_1, t_2$ the two times in years, $t_1 < t_2$

Worked example

A sum at simple interest amounts to ₹2,360 in 3 years and to ₹2,600 in 5 years. Find the sum and the rate.

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 23 Sep 2025, Shift 2 · Q53Easy

Example 2 · Simple and Compound Interest · Finding the Rate, Time or Principal

A sum amounts to ₹6,600 in 2 years and ₹7,200 in 4 years at simple interest. What is the rate of interest per annum?

Dividing the rise by the later time

The rise between the two amounts covers only the years between them. From ₹2,240 at 3 years to ₹2,400 at 5 years, one year earns

\frac{160}{2} = 80

, not

\frac{160}{5}

Drill 3 more on two amounts after two different times

Concept 3 of 4: Equal simple interest on two sums

Interest depends on principal, rate and time together. Two loans earn the same interest when the product of the three is the same, so a smaller sum needs a higher rate or more years.

Definition

Equal interest: $\frac{P_1 R_1 T_1}{100} = \frac{P_2 R_2 T_2}{100}$ , so $P_1 R_1 T_1 = P_2 R_2 T_2$ . The 100s cancel.
Put in the five known numbers and solve for the sixth.
Ratio of the sums: $\frac{P_1}{P_2} = \frac{R_2 T_2}{R_1 T_1}$ . The sum with the smaller rate times time is the larger sum.

Equal simple interest

P_1 R_1 T_1 = P_2 R_2 T_2

Worked example

In how many years will ₹6,000 at 5% per annum earn the same simple interest as ₹4,000 earns in 6 years at 10% per annum?

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 21 Sep 2025, Shift 3 · Q53Easy

Example 3 · Simple and Compound Interest · Finding the Rate, Time or Principal

If the simple interest on a sum of Rs. A at 6% per annum for 2 years is equal to the simple interest on Rs. B at 4% per annum for 3 years, then what is the ratio of A to B?

Turning the ratio of sums upside down

For equal interest the sums are in the inverse ratio of rate times time. If one loan runs at rate times time 12 and the other at 24, the first sum is twice the second, not half.

Drill 4 more on equal simple interest on two sums

Concept 4 of 4: Rate tied to the number of years

When the stem links the rate to the time, there is really only one unknown. Write both with one letter and the formula gives its square.

Definition

If the time in years equals the rate percent, $SI = \frac{P \times R \times R}{100}$ , so $R^2 = \frac{100 \times SI}{P}$ .
If the rate is $k$ times the years (or the years are $k$ times the rate), write both through one letter and solve the square in the same way.
Take the positive square root, then read the question again: it may ask for the time, not the rate.

Rate equal to the years

R^2 = \frac{100 \times SI}{P}

Worked example

₹2,500 is borrowed at simple interest for as many years as the rate percent. The interest is ₹625. Find the rate.

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 18 Sep 2025, Shift 2 · Q57Easy

Example 4 · Simple and Compound Interest · Finding the Rate, Time or Principal

Reena borrowed Rs. 1200 at simple interest for a number of years equal to the rate of interest. At the end of the loan term, she paid Rs. 432 in interest. What was the interest rate?

Answering the time when the rate is asked

When the rate is a multiple of the years, the options print both numbers. If the time is four times the rate, a 3% rate means 12 years, and both 3 and 12 sit among the options: check which one the question wants.

Drill 2 more on rate tied to the number of years

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 (4)

Finding the rate or the time from the interest
Rate, time and principal
$R = \frac{100 \times SI}{P \times T} \qquad T = \frac{100 \times SI}{P \times R} \qquad P = \frac{100 \times SI}{R \times T}$
Two amounts after two different times
Two amounts at two times
$\text{Interest per year} = \frac{A_2 - A_1}{t_2 - t_1} \qquad P = \frac{t_2 A_1 - t_1 A_2}{t_2 - t_1}$
Equal simple interest on two sums
Equal simple interest
$P_1 R_1 T_1 = P_2 R_2 T_2$
Rate tied to the number of years
Rate equal to the years
$R^2 = \frac{100 \times SI}{P}$

Watch out for (5)

Using the amount as the interest
→ Finding the rate or the time from the interest
Rounding the rate too early
→ Finding the rate or the time from the interest
Dividing the rise by the later time
→ Two amounts after two different times
Turning the ratio of sums upside down
→ Equal simple interest on two sums
Answering the time when the rate is asked
→ Rate tied to the number of years

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 28 questions