Lesson 40 of 100 | Quantitative Aptitude / Simple Interest / साधारण ब्याज
Principal, rate, time, simple interest and amount
Learning outcome
Identify principal, annual rate and time, then calculate simple interest and the final amount using compatible units.
Concepts and assumptions
Principal P is the original sum. Interest I is the additional sum earned or charged under the stated calculation. Amount A is principal plus interest: A = P + I. Interest alone is not the amount.
For simple interest, every year’s interest uses the original principal, not the previous year’s amount. If the annual rate is r%, one year’s interest is P × r/100. Time scales this fixed yearly quantity:
I = P × r × t ÷ 100, where t is measured in years.
A = P × (1 + r × t/100).
These formulas work because equal time intervals generate equal interest while principal and rate remain unchanged. Unpaid simple interest does not itself earn interest.
Assume P > 0, a nonnegative annual rate, no extra deposits, withdrawals, interim payments or fees. The rate stays fixed unless a question states otherwise. Use 12 months per year and a stipulated 365-day year for day-based questions; do not assume every month has 30 days. Convert months using months ÷ 12 and days using days ÷ 365.
Keep intermediate calculations exact. Round final money only to the nearest ₹0.01 when necessary, with half a paise rounded upward.
Worked examples
Example 1 — One year. Find interest and amount on ₹6,500 at 8% per year for one year. Annual interest = 6500 × 8 ÷ 100 = ₹520. Therefore I = ₹520 and A = 6500 + 520 = ₹7,020. The amount contains both the original sum and interest.
Example 2 — Convert months. Find the results on ₹8,400 at 7.5% for 18 months. Time = 18 ÷ 12 = 1.5 years. I = 8400 × 7.5 × 1.5 ÷ 100 = ₹945. Therefore A = 8400 + 945 = ₹9,345. Using 18 as the time in years would overstate the interest.
Example 3 — Use a day convention. Find the results on ₹18,250 at 8% for 73 days, using a 365-day year. Annual interest = 18250 × 8 ÷ 100 = ₹1,460. Time = 73/365 = 1/5 year. Thus I = 1460 × 1/5 = ₹292 and A = 18250 + 292 = ₹18,542.
Common mistakes
Do not mix an annual rate with unconverted months or days. Do not add interest to the next year’s interest base. A different stated day-year convention would require a different denominator.
Practice questions
- Find interest and amount on ₹4,800 at 9% simple interest for 2 years.
- Find interest and amount on ₹12,500 at 6% for 8 months.
- Find interest and amount on ₹10,950 at 5% for 40 days using a 365-day year.
- ₹9,200 earns 5% simple interest annually. Find the interest generated during the second year and the amount after 2 years.
Worked answers
- I = 4800 × 9 × 2 ÷ 100 = ₹864. Add the principal: A = 4800 + 864 = ₹5,664.
- Time = 8/12 = 2/3 year. I = 12500 × 6 × (2/3) ÷ 100 = ₹500; A = ₹13,000.
- Time = 40/365 year. I = 10950 × 5 × (40/365) ÷ 100 = ₹60; A = ₹11,010.
- Second-year interest still uses ₹9,200: 9200 × 5 ÷ 100 = ₹460. Two years generate 2 × 460 = ₹920, so A = ₹10,120.