Episode 8 — Aptitude and Reasoning / 8.3 — Simple Interest
8.3 Quick Revision -- Simple Interest
Use this sheet for a rapid refresh before exams. Everything you need on one page.
1. All Formulas at a Glance
+═══════════════════════════════════════════════════════════════+
| CORE FORMULAS |
+═══════════════════════════════════════════════════════════════+
| |
| Simple Interest: SI = (P x R x T) / 100 |
| |
| Amount: A = P + SI |
| A = P x (100 + RT) / 100 |
| |
| Principal: P = (SI x 100) / (R x T) |
| P = (A x 100) / (100 + RT) |
| |
| Rate: R = (SI x 100) / (P x T) |
| |
| Time: T = (SI x 100) / (P x R) |
| |
+═══════════════════════════════════════════════════════════════+
| MULTIPLIER FORMULAS |
+═══════════════════════════════════════════════════════════════+
| |
| Amount = n times P: R x T = (n - 1) x 100 |
| Doubles (n=2): R x T = 100 |
| Triples (n=3): R x T = 200 |
| Quadruples (n=4): R x T = 300 |
| |
| Time for n times = (n-1) x (time to double) |
| |
+═══════════════════════════════════════════════════════════════+
| SPECIAL SCENARIOS |
+═══════════════════════════════════════════════════════════════+
| |
| Varying rates: SI = P(R1.T1 + R2.T2 + R3.T3) / 100 |
| |
| Lending profit: Gain = P(R_lend - R_borrow) x T / 100 |
| |
| Equal SI: P1.R1.T1 = P2.R2.T2 |
| |
| Two amounts at different times (same P, R): |
| SI/year = (A2 - A1) / (T2 - T1) |
| P = A1 - (SI/year x T1) |
| |
| Annual deposits for n years: |
| Total SI = P x R/100 x n(n+1)/2 |
| |
| CI - SI for 2 years: P x (R/100)^2 |
| |
+═══════════════════════════════════════════════════════════════+
2. Doubling Time Table (Memorize)
Rate (%) | Time to Double | Time to Triple
──────────┼──────────────────┼──────────────────
5 | 20 years | 40 years
8 | 12.5 years | 25 years
10 | 10 years | 20 years
12 | 8.33 years | 16.67 years
12.5 | 8 years | 16 years
15 | 6.67 years | 13.33 years
20 | 5 years | 10 years
25 | 4 years | 8 years
3. Fraction Equivalents for Common Rates
Rate (%) Fraction Quick Method
────────────────────────────────────────
5 1/20 Divide P by 20
6.25 1/16 Divide P by 16
8 2/25 P x 2 / 25
8.33 1/12 Divide P by 12
10 1/10 Divide P by 10
12.5 1/8 Divide P by 8
16.67 1/6 Divide P by 6
20 1/5 Divide P by 5
25 1/4 Divide P by 4
33.33 1/3 Divide P by 3
50 1/2 Divide P by 2
4. Time Conversion Quick Reference
Months -> Years: Divide by 12
Days -> Years: Divide by 365
Common conversions:
1 month = 1/12 yr 73 days = 1/5 yr
2 months = 1/6 yr 146 days = 2/5 yr
3 months = 1/4 yr 219 days = 3/5 yr
4 months = 1/3 yr 292 days = 4/5 yr
6 months = 1/2 yr 365 days = 1 yr
8 months = 2/3 yr
9 months = 3/4 yr
18 months = 3/2 yr
5. Shortcut Table
Situation Shortcut
──────────────────────────────────────────────────────────────
Find SI quickly Calc for 1 year, multiply by T
Rate is a fraction (12.5% = 1/8) Divide P by denominator
Amount doubles R x T = 100
Amount becomes n times R x T = (n-1) x 100
Time for n times from doubling time (n-1) x T_double
Profit on lending/borrowing P x (Rate diff) x T / 100
SI at two rates, diff given P = (Diff x 100) / (Rate diff x T)
Two amounts at different times SI/yr = (A2-A1)/(T2-T1)
Equal SI, two investments P1.R1.T1 = P2.R2.T2
Split into two parts (alligation) Find effective rate, use ratio
SI = fraction of P (say k.P) R x T = k x 100
4% more rate -> Rs.X more interest P = X x 100 / (4 x T)
6. Common Patterns in Exam Questions
Pattern 1: "A sum doubles in T years. In how many years will it triple?"
--> Answer: 2T years
Pattern 2: "Difference between SI at two rates for same P and T"
--> P = (Diff x 100) / ((R1 - R2) x T)
Pattern 3: "Sum becomes X in T1 years and Y in T2 years"
--> SI per year = (Y - X)/(T2 - T1), then find P
Pattern 4: "Borrows at R1% and lends at R2%"
--> Gain = P(R2 - R1) x T / 100
Pattern 5: "Split Rs. S into two parts at R1% and R2%"
--> Two equations, one unknown. Or use alligation.
Pattern 6: "SI is what fraction of P?"
--> SI/P = RT/100
Pattern 7: "Amount is n/m of P"
--> SI = (n/m - 1) x P, then find R or T
Pattern 8: "Equal annual deposits for n years"
--> Total SI = Deposit x R/100 x [n + (n-1) + ... + 1]
7. Five-Second Mental Math Checks
10% of any number: Move decimal one place left.
10% of 4500 = 450
5% of any number: Half of 10%.
5% of 4500 = 225
1% of any number: Move decimal two places left.
1% of 4500 = 45
8% of any number: 10% minus 2%.
8% of 4500 = 450 - 90 = 360
12% of any number: 10% plus 2%.
12% of 4500 = 450 + 90 = 540
15% of any number: 10% plus 5%.
15% of 4500 = 450 + 225 = 675
25% of any number: Divide by 4.
25% of 4500 = 1125
8. Common Traps to Avoid
[!] Time not in years -- ALWAYS convert months/days to years first.
[!] Question asks Amount, you give SI (or vice versa).
[!] "Per half-year" or "per quarter" -- convert to per annum, or
adjust the time period accordingly.
[!] Confusing SI and CI formulas. SI is LINEAR.
SI: A = P + PRT/100
CI: A = P(1 + R/100)^T <-- Different!
[!] In split problems, not reading which part to report.
[!] Forgetting: for SI, frequency of interest calculation
does NOT matter. Annual/half-yearly/quarterly all give same SI.
9. Last-Minute Mnemonics
SI = PRT / 100 --> "Principal's Rate over Time, all over Hundred"
Doubling: R x T = 100
"Rate times Time equals a century for doubles"
Amount = P + SI --> "A is Always P plus Something Interesting"
Finding P from A: P = A x 100 / (100 + RT)
"Principal is Amount scaled down"
10. Key Differences: SI vs CI (Quick Comparison)
Feature | Simple Interest | Compound Interest
─────────────────┼───────────────────────┼───────────────────
Calculated on | Original principal | Accumulated amount
Growth | Linear (straight) | Exponential (curved)
Year 1 interest | Same as all years | Starting point
Year 2+ interest | Same as year 1 | Increases each year
For T = 1 | SI = CI | SI = CI
For T = 2 | SI < CI | CI > SI
Difference (T=2) | -- | P(R/100)^2
Good luck with your exam!
Back to: README | Concepts | Tips & Tricks | Solved Examples | Practice MCQs