Simple interest
SI = P x R x T / 100. Interest is the same every year because it is always on the original principal.
P 5000 at 8% for 3 years: SI = 5000 x 8 x 3 / 100 = 1200.
Rapid Revision · Quantitative Aptitude
Simple & Compound Interest
SI grows in a straight line, CI grows on itself. Most questions test whether you can switch between the two formulas and spot compounding periods.
The 3-minute recap
If you read nothing else tonight, read these 6 lines.
- SI = P x R x T / 100; amount = P + SI.
- CI amount = P x (1 + r/100)^t; CI = amount - P.
- CI - SI over 2 years = P x (r/100)^2.
- Half-yearly compounding: halve the rate, double the periods.
- Two years at r% compound = single change of 2r + r^2/100 percent.
- SI doubling time: T = 100/R years.
Formula sheet
Every formula for simple & compound interest in one place, each labelled so you know exactly when to reach for it. Screenshot it the night before.
Simple interest
SI = (P x R x T) / 100 Amount = P + SI
Compound interest
A = P x (1 + R/100)^n CI = A - P
Compounding k times a year
A = P x (1 + R/(100k))^(n x k)
Half-yearly k=2, quarterly k=4.
CI - SI over 2 years
difference = P x (R/100)^2
Fast way to back out P or R from the gap.
CI - SI over 3 years
difference = P x (R/100)^2 x (3 + R/100)
Doubling (rule of 72)
years to double ~ 72 / R%
Quick CI estimate, not exact.
Work through the cards
7 cards, each one idea: what it is, a worked example, and the trap to dodge.
Compound amount
Amount = P x (1 + r/100)^t. Each year's interest joins the principal for the next year.
1000 at 10% for 2 years: 1000 x 1.1 x 1.1 = 1210, so CI = 210.
Trap: CI questions often ask for the INTEREST; subtract P from the amount.
CI vs SI gap
For 2 years, CI - SI = P x (r/100)^2. For 3 years, CI - SI = P x (r/100)^2 x (3 + r/100).
P 10000, r 10%, 2 years: difference = 10000 x 0.01 = 100.
Trap: In year 1, CI equals SI; the gap starts from year 2.
Compounding more often
Half-yearly: rate/2, periods x2. Quarterly: rate/4, periods x4.
20% annual, 1 year half-yearly: 10% twice = 21% effective.
Trap: Change BOTH the rate and the number of periods, not just one.
Successive-change shortcut for CI
Two years at r% is the successive change r then r: net = 2r + r^2/100 percent. Fast for 2-year mental math.
r = 10: 20 + 1 = 21% growth over 2 years.
Doubling and tripling
SI: money doubles when SI = P, so T = 100/R years. CI: if money doubles in t years, it becomes 4x in 2t and 8x in 3t years.
CI doubles in 5 years: 8x takes 15 years.
Trap: Do not apply the SI doubling formula to CI questions.
Rate or time from two amounts
Under CI, amounts t years apart are in ratio (1 + r/100)^t. Divide the two amounts to isolate the rate.
Amount 1210 after 2 years, 1331 after 3: ratio 1.1, so r = 10% and P = 1000.
Go deeper
A recap is not practice. These are the creators we rate for real depth on simple & compound interest; full credit to each.
One topic down. Keep the streak going.
Each recap takes 3 minutes; the full set covers everything the first round tests. And when the test is cleared, your resume takes the next screen.
Original content by OptiResume; facts and formulas are common knowledge, the wording is ours. Go-deeper links go to creators we rate; we are not affiliated with them.