Simple Interest • Topic 2 of 3

Interest & Amount

The Amount is what the borrower finally repays: A = P + SI = P(1 + RT/100). CAT problems often hand you the amount after one period and the amount after another and ask you to recover P and R together. The clean trick: since interest is constant each year under SI, the difference between two amounts is purely interest. If a sum amounts to A₁ in T₁ years and A₂ in T₂ years, then one year’s interest = (A₂ − A₁)/(T₂ − T₁); multiply by T₁ to get the interest in T₁ years, subtract from A₁ to get the principal, then back out the rate. This two-amount method avoids simultaneous equations entirely. Watch the phrasing: "amounts to" means principal plus interest, while "interest is" means just the SI part — confusing them flips your answer.

✅ Solved examples

1. Find the amount on ₹10,000 at 12% per annum simple interest for 3 years.
SI = 10000 × 12 × 3/100 = ₹3,600. Amount = P + SI = 10000 + 3600 = ₹13,600.
2. A sum amounts to ₹7,200 in 2 years and ₹7,800 in 3 years at simple interest. Find the principal and rate.
One year’s interest = 7800 − 7200 = ₹600. In 2 years interest = ₹1,200, so P = 7200 − 1200 = ₹6,000. R = 100 × 600/(6000 × 1) = 10% per annum.
3. A sum doubles its principal as amount in 8 years under simple interest. Find the rate.
Amount = 2P means SI = P. So P = P×R×8/100 ⇒ R = 100/8 = 12.5% per annum.
4. The amount on ₹4,500 for 4 years is ₹6,300. Find the rate of simple interest.
SI = 6300 − 4500 = ₹1,800. R = 100 × 1800/(4500 × 4) = 180000/18000 = 10% per annum.

✏️ Practice — try these, take hints as needed

1. Find the amount on ₹16,000 at 8% per annum SI for 5 years.
SI = PRT/100 first.
16000 × 8 × 5/100 = 6400.
Add to principal.
₹22,400
2. A sum amounts to ₹9,440 in 3 years and ₹10,400 in 5 years at SI. Find the principal.
Interest for 2 years = 10400 − 9440.
One year = 960/2 = 480.
3 years interest = 1440; P = 9440 − 1440.
₹8,000
3. A sum trebles itself (amount = 3P) in 16 years at SI. Find the rate.
Amount 3P means SI = 2P.
2P = P×R×16/100.
R = 200/16.
12.5% per annum
4. The amount on ₹12,500 at 6% per annum SI is ₹15,500. For how many years?
SI = 15500 − 12500 = 3000.
T = 100·SI/(P·R).
100 × 3000/(12500 × 6).
4 years
5. A sum amounts to ₹2,640 in 2 years and ₹3,000 in 5 years at SI. Find the rate.
Interest for 3 years = 3000 − 2640 = 360.
One year = 120; 2-year interest = 240; P = 2640 − 240 = 2400.
R = 100 × 120/2400.
5% per annum

📝 Topic test — 8 questions

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