2.1 Simple Interest — Formula and Rearrangements

Simple Interest is interest calculated only on the original principal, for every time period, at a fixed rate. It never compounds — the interest earned in one period does not itself earn further interest.

Basic formula:

SI = (P × R × T)/(100)

where P = Principal (initial sum invested/borrowed), R = rate of interest per annum (%), T = time in years.

Amount: A = P + SI = P(1 + (RT)/(100))

Rearrangements (memorise all four — SSC frequently asks for P, R, or T given the rest):

P = (SI × 100)/(R × T) R = (SI × 100)/(P × T) T = (SI × 100)/(P × R)

A key structural fact: under SI, the amount grows linearly with time — equal amounts of interest are added every year. This is what distinguishes it from CI, where growth is compounded (multiplicative).

These four rearrangements are the true foundation of the entire chapter — nearly every “find the missing quantity” SI question, no matter how it is worded (percentage growth, “borrowed and repaid”, “invested and matured”), reduces to picking the correct rearrangement and substituting the three known values. Practice identifying which of P, R, T, or SI is missing within the first five seconds of reading the question, before you even reach for your pen.

Solved Example 2.1.1: Find the SI and the amount on Rs. 7,500 at 8% p.a. for 4 years.

Solution: SI = (7500 × 8 × 4)/100 = Rs. 2,400. Amount = 7500 + 2400 = Rs. 9,900.

Solved Example 2.1.2: At what rate percent per annum will Rs. 4,000 yield an SI of Rs. 960 in 4 years?

Solution: R = (SI × 100)/(P × T) = (960 × 100)/(4000 × 4) = 96000/16000 = 6% p.a.

Solved Example 2.1.3: A sum of money amounts to Rs. 16,800 in 4 years at simple interest starting from a principal of Rs. 12,000. Find the rate of interest.

Solution: SI = 16800 − 12000 = Rs. 4,800. R = (4800 × 100)/(12000 × 4) = 480000/48000 = 10% p.a.

Solved Example 2.1.4: In how many years will Rs. 8,000 amount to Rs. 10,400 at 6% p.a. simple interest?

Solution: SI = 10400 − 8000 = Rs. 2,400. T = (SI × 100)/(P × R) = (2400 × 100)/(8000 × 6) = 240000/48000 = 5 years.

Solved Example 2.1.5: A sum of money becomes 7/4 times of itself in 5 years at simple interest. Find the rate of interest.

Solution: If the amount is 7/4 P, then SI = (7/4)P − P = (3/4)P. Using R = (SI × 100)/(P × T): R = [(3/4)P × 100]/(P × 5) = 75/5 = 15% p.a. Notice this is exactly the ratio-shortcut style of Trick 4 applied to a fractional multiple instead of a decimal one — always convert the fraction to “how much extra” (here 3/4 of P) before plugging into the rate formula.