A sum at simple interest amounts to ₹7,200 in 2 years and ₹8,400 in 4 years. Find the principal and the rate.
Principal ₹6,000 and rate 10% per year. Two extra years added ₹1,200, so yearly interest is ₹600. Two years of interest is ₹1,200, so P = 7,200 - 1,200 = ₹6,000, and R = 600/6,000 = 10%.
Explain it simply
Simple interest is like a fixed monthly stipend: the same amount is added every year. The difference between two amounts tells you how much one year adds. Then go back from either amount, removing that yearly interest as many times as there are years, and you reach the principal.
Example
Question: Amount = ₹7,200 after 2 years and ₹8,400 after 4 years at SI.
- Interest for 2 years (years 3 and 4) = 8,400 - 7,200 = ₹1,200.
- Interest per year = ₹600.
- Interest for the first 2 years = ₹1,200, so P = 7,200 - 1,200 = ₹6,000.
- R = 600 / 6,000 x 100 = 10%.
Check: 6,000 + 4 x 600 = 8,400. Correct.
const yearly = (8400 - 7200) / 2;
const P = 7200 - 2 * yearly;
console.log(P); // Output: 6000
console.log((yearly / P) * 100); // Output: 10Compare with compound interest, where you would divide the amounts instead of subtracting them.
What to say in the interview
"Under simple interest the amount rises by the same interest every year. 1,200 in two years is 600 a year. Taking two years off 7,200 gives the principal, 6,000, so the rate is 10 percent."
Common mistakes
- Taking the rate on ₹7,200 instead of the principal.
- Dividing amounts as you would for compound interest.