Simple Interest
Simple Interest
Simple interest (SI) is charged only on the original principal, so the interest is the same every year. That one fact turns most NTPC SI questions into a straight-line calculation: the yearly interest is a constant step. NTPC asks the basic formula, "doubles in n years", amounts after two different times, a change in rate, and a sum split at two rates.
1. Formula Box
SI = (P × R × T)/100 Amount A = P + SI = P(1 + RT/100)
P = (100 × SI)/(R × T) R = (100 × SI)/(P × T) T = (100 × SI)/(P × R)
| Term | Meaning | Unit trap |
|---|---|---|
| P | Principal (sum lent) | In rupees |
| R | Rate per year | Rate per month × 12 = rate per year (2% per month = 24% p.a.) |
| T | Time in years | 6 months = 1/2 year; 73 days = 1/5 year (365-day year) |
| SI per year | P × R/100 | Constant every year under SI |
2. Shortcut Rules
| Situation | Rule | Example |
|---|---|---|
| Sum becomes n times in T years | R = (n − 1) × 100/T | Doubles in 8 years: R = 100/8 = 12.5% |
| Doubles in T years, becomes k times in? | Time = (k − 1) × T | Doubles in 6 years, becomes 4 times in 18 years |
| Amounts A₁ after T₁ and A₂ after T₂ years | SI per year = (A₂ − A₁)/(T₂ − T₁); P = A₁ − T₁ × yearly SI | 8,280 (3 y), 9,000 (5 y): 360 per year, P = 7,200 |
| Rate up by r% | Extra SI = P × r × T/100 | ₹3,000 at 3% more for 4 years = ₹360 extra |
| Different rates in different periods | Add the rate-years: SI = P × (R₁T₁ + R₂T₂ + ...)/100 | 6% for 2 y + 8% for 3 y = 36% of P |
| Sum split so interests are equal | Parts are in the ratio 1/(R₁T₁) : 1/(R₂T₂) | 8% for 3 y and 6% for 5 y: parts 1/24 : 1/30 = 5 : 4 |
✗ Doubles in 8 years, so 4 times in 16 years | ✓ Under SI growth is linear: doubling adds 1P every 8 years, so 4 times (3P interest) takes 24 years
✗ Rate 2% per month for 6 months = 2% | ✓ Convert: 2% per month = 24% p.a.; for 1/2 year SI = 12% of P
हिंदी नोट: साधारण ब्याज में हर साल का ब्याज बराबर होता है, इसलिए दो समयों की राशि का अंतर सीधे सालाना ब्याज बता देता है। मासिक दर को 12 से गुणा करके वार्षिक दर बनाइए।
Exam Pointer: Verified NTPC patterns: basic SI, including SI against the sum (March 2021, June 2025 Graduate CBT-1) and a per-month rate (August 2025 UG CBT-1); sum becoming n times (March 2021, June 2022 CBT-2); amounts after two different periods (two June 2025 Graduate CBT-1 shifts); extra interest when the rate rises (March 2021, June 2022 CBT-2); and a sum split for equal interest (August 2025 UG CBT-1). Rate slabs over periods are tagged syllabus-based.
Pariksha Pattern: Every Way NTPC Asks This Topic
Pattern 1: Basic SI: find interest, principal, rate or time
[PYQ: NTPC CBT-1 27-Mar-2021 Shift-1 | NTPC Graduate CBT-1 17-Jun-2025 Shift-1 | NTPC UG CBT-1 22-Aug-2025 Shift-2]
EXAM LEVEL
Q. Find the simple interest and the amount on ₹12,500 at 8% per annum for 3 years 6 months.
T = 3.5 years. SI = 12,500 × 8 × 3.5/100 = ₹3,500. Amount = 12,500 + 3,500 = ₹16,000.
Answer: SI ₹3,500; amount ₹16,000
EXAMATLAS LEVEL
Q. A sum is lent at 5% simple interest per annum for 9 years. The interest is ₹4,950 less than the sum. Find the sum.
Interest = 5 × 9 = 45% of the sum, so the sum exceeds the interest by 55% of itself. 55% = 4,950, giving the sum = ₹9,000. Check: SI = ₹4,050, and 9,000 − 4,050 = 4,950.
Answer: ₹9,000
Pattern 2: A sum becomes n times under SI
[PYQ: NTPC CBT-1 14-Mar-2021 Shift-1 | NTPC CBT-2 15-Jun-2022 Shift-3]
EXAM LEVEL
Q. At what rate of simple interest will a sum double itself in 8 years?
Doubling means SI = P in 8 years, so R = 100/8 = 12.5% per annum.
Answer: 12.5%
EXAMATLAS LEVEL
Q. A sum becomes 7/4 of itself in 6 years at simple interest. In how many years will it become 5/2 of itself?
In 6 years the interest is 3/4 of P. Needed interest is 3/2 of P, which is twice as much, so twice the time: 12 years. (Rate = (3/4)/6 × 100 = 12.5%.)
Answer: 12 years
Pattern 3: Amounts after two different periods
[PYQ: NTPC Graduate CBT-1 16-Jun-2025 Shift-1 | NTPC Graduate CBT-1 16-Jun-2025 Shift-2]
EXAM LEVEL
Q. A sum amounts to ₹8,280 in 3 years and to ₹9,000 in 5 years at simple interest. Find the sum and the rate.
Two extra years add 9,000 − 8,280 = ₹720, so SI per year = ₹360. Three years' SI = ₹1,080, so P = 8,280 − 1,080 = ₹7,200. Rate = 360/7,200 × 100 = 5%.
Answer: ₹7,200 at 5%
EXAMATLAS LEVEL
Q. A sum amounts to ₹5,800 in 2 years and ₹7,000 in 5 years at simple interest. Find the principal, the rate, and the time in which it will amount to ₹9,000.
Yearly SI = (7,000 − 5,800)/3 = ₹400. P = 5,800 − 800 = ₹5,000, rate = 400/5,000 × 100 = 8%. For ₹9,000 the interest needed is ₹4,000, which takes 4,000/400 = 10 years.
Answer: ₹5,000; 8%; 10 years
Pattern 4: A change in rate changes the interest
[PYQ: NTPC CBT-2 13-Jun-2022 Shift-2 | NTPC CBT-1 4-Mar-2021 Shift-1]
EXAM LEVEL
Q. Had the rate of simple interest been 3% higher, a sum would have earned ₹360 more in 4 years. Find the sum.
Extra SI = P × 3 × 4/100 = 0.12P = 360, so P = ₹3,000.
Answer: ₹3,000
EXAMATLAS LEVEL
Q. ₹4,800 amounts to ₹5,760 in 4 years at simple interest. What will it amount to in the same time if the rate is increased by 2.5%?
SI = 960 in 4 years, so the rate = 960 × 100/(4,800 × 4) = 5%. New rate 7.5%: SI = 4,800 × 7.5 × 4/100 = ₹1,440, amount ₹6,240. Shortcut: extra = 4,800 × 2.5 × 4/100 = 480, so 5,760 + 480 = 6,240.
Answer: ₹6,240
Pattern 5: A sum split at two rates
[PYQ: NTPC UG CBT-1 13-Aug-2025 Shift-2]
EXAM LEVEL
Q. ₹12,000 is lent partly at 8% and partly at 10% simple interest. The total interest for one year is ₹1,100. How much is lent at 8%?
If all were at 10%, interest = ₹1,200. Each rupee moved to 8% loses 2 paise: 1,200 − 1,100 = 100 = 0.02x, so x = ₹5,000 at 8% and ₹7,000 at 10%.
Answer: ₹5,000
EXAMATLAS LEVEL
Q. ₹16,200 is divided into two parts so that the simple interest on the first at 8% for 3 years equals the simple interest on the second at 6% for 5 years. Find the parts.
24% of the first = 30% of the second, so the parts are in the ratio 30 : 24 = 5 : 4. First = 16,200 × 5/9 = ₹9,000, second = ₹7,200. Check: 2,160 = 2,160.
Answer: ₹9,000 and ₹7,200
Pattern 6: Different rates over different periods
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. ₹20,000 is borrowed at 6% simple interest for the first 2 years and 8% for the next 3 years. Find the total interest.
Rate-years = 6 × 2 + 8 × 3 = 36, so SI = 36% of 20,000 = ₹7,200.
Answer: ₹7,200
EXAMATLAS LEVEL
Q. A sum is lent at 5% for the first 3 years, 7% for the next 2 years and 9% beyond 5 years, all simple interest. The total interest after 7 years is ₹7,050. Find the sum.
Rate-years = 15 + 14 + 18 = 47, so 47% of P = 7,050 and P = ₹15,000.
Answer: ₹15,000
60-Second Revision
- SI = PRT/100; yearly SI is constant; per-month rate × 12 = annual rate.
- n times in T years: R = (n − 1) × 100/T; time scales with (n − 1).
- Two amounts: difference ÷ gap in years = yearly SI; then P = A₁ − T₁ × yearly SI.
- Rate up by r%: extra = P × r × T/100.
- Rate slabs: add rate × years; equal-interest split: parts in ratio 1/(R₁T₁) : 1/(R₂T₂).