At a certain annual rate (rounded off to the nearest integer) of simple interest, a sum of money becomes nine times its original value in 21 years. By how much does the rate of interest change if the same sum of money has to become 12 times its original value in 25 years?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. Increase by 6%.
The amount becomes nine times the principal, so the simple interest is 9P - P = 8P
Simple Interest (SI) = (P × R × T)/100
⇒ 8P = (P × R × 21)/100
⇒ R = (8 × 100)/21 = 38.095 ≈ 38%
The amount becomes 12 times the principal, so the simple interest is 12P - P = 11P
So, 11P = (P × R1 × 25)/100
⇒ 11 = (R1 × 25)/100 = R1/4
⇒ R1 = 44%
Change in rate = 44% - 38% = 6%
Therefore, the rate of interest changes by 6%.