A sum doubles itself in 8 years at simple interest. What is the rate, and in how many years will it become three times?

Under simple interest you earn the same amount every year, always calculated on the original sum. "Doubles" means the interest earned equals the principal, so the interest is 100% of the principal. "Triples" means the interest is 200% of the principal. Because simple interest grows in a straight line, twice the interest needs twice the time.

Question: A sum doubles in 8 years at SI. Find the rate and the time to triple.

1. Let P = ₹100. It becomes ₹200, so SI = ₹100 in 8 years.
2. SI = P x R x T / 100 gives 100 = 100 x R x 8 / 100, so R = 100 / 8 = 12.5%.
3. To triple: SI = ₹200. 200 = 100 x 12.5 x T / 100, so T = 16 years.

Pattern: if a sum becomes n times in T years at SI, it becomes m times in T x (m - 1) / (n - 1) years. Here 8 x (3 - 1) / (2 - 1) = 16.

const R = 100 / 8;
console.log(R); // Output: 12.5
console.log(200 / R); // Output: 16

Do not use this for compound interest. At CI a sum that doubles in 8 years becomes four times in 16 years, not three times.

• Thinking tripling takes 24 years (3 x 8); only the interest part grows, and it needs 2 x 8.
• Mixing this rule up with compound interest, where the amount multiplies.