An amount increases by 50% in 5 years at simple interest. What will be the…
2023
An amount increases by 50% in 5 years at simple interest. What will be the compound interest on ₹12,000 after 3 years at the same annual rate?
Answer: A. ₹3,972 — ConceptUnder simple interest, interest grows linearly with time. Therefore, if a principal gains x% in t years, the annual rate is (x/t)% per year. For annual…
- A.
₹3,972
- B.
₹6,240
- C.
₹3,120
- D.
More than one of the above
- E.
None of the above
Attempted by 1 students.
Show answer & explanation
Correct answer: A
Concept
Under simple interest, interest grows linearly with time. Therefore, if a principal gains x% in t years, the annual rate is (x/t)% per year.
For annual compounding, the amount after n years is A = P(1 + r/100)n, and the compound interest is CI = A − P.
Application
A 50% simple-interest increase in 5 years gives the annual rate r = 50/5 = 10%.
Use P = ₹12,000, r = 10, and n = 3 in the compound-amount formula.
A = ₹12,000 × (1.10)3 = ₹15,972.
CI = A − P = ₹15,972 − ₹12,000 = ₹3,972.
Cross-check
The interest earned year by year is ₹1,200, ₹1,320, and ₹1,452; their sum is ₹3,972, confirming the result.