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

1. Find interest and amount on ₹4,800 at 9% simple interest for 2 years.
2. Find interest and amount on ₹12,500 at 6% for 8 months.
3. Find interest and amount on ₹10,950 at 5% for 40 days using a 365-day year.
4. ₹9,200 earns 5% simple interest annually. Find the interest generated during the second year and the amount after 2 years.

Worked answers

1. I = 4800 × 9 × 2 ÷ 100 = ₹864. Add the principal: A = 4800 + 864 = ₹5,664.
2. Time = 8/12 = 2/3 year. I = 12500 × 6 × (2/3) ÷ 100 = ₹500; A = ₹13,000.
3. Time = 40/365 year. I = 10950 × 5 × (40/365) ÷ 100 = ₹60; A = ₹11,010.
4. Second-year interest still uses ₹9,200: 9200 × 5 ÷ 100 = ₹460. Two years generate 2 × 460 = ₹920, so A = ₹10,120.