A sum of money becomes five times its original value in 15 years when invested at a certain simple interest rate. If the sum was invested twice the time at the same rate of interest, what would be the final amount?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. The money becomes 9 times its original value.
We know that,
A = P(1 + RT/100)
here, A = Amount, P = Principal, R = rate, and T = Time
The amount becomes 5 times the principal in 15 years
A = 5P
⇒ 5P = P(1 + 15R/100)
⇒ 5 = 1 + 15R/100
⇒ 5 - 1 = 15R/100
⇒ 4 = 15R/100
⇒ R = 400/15
⇒ R = 26.67%
If the time is doubled, T = 2 × 15 = 30 years
⇒ A = P(1 + RT/100)
⇒ A = P(1 + 26.67 × 30/100)
⇒ A = P(1 + 800.1/100)
⇒ A = P(1 + 8.001)
⇒ A = 9.001P
Thus, The final amount will be approximately 9 times the original principal