Question
Download Solution PDFA 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A sum of money becomes five times its original value in 15 years at a certain simple interest rate.
Formula used:
Simple Interest (SI) = P × R × T / 100
Amount (A) = Principal (P) + Simple Interest (SI)
Calculation:
Let the Principal be P.
Amount after 15 years = 5P
⇒ 5P = P + (P × R × 15 / 100)
⇒ 5P = P + 15PR / 100
⇒ 5P - P = 15PR / 100
⇒ 4P = 15PR / 100
⇒ R = (4P × 100) / (15P)
⇒ R = 400 / 15
⇒ R = 80 / 3 %
If the sum is invested for twice the time (30 years) at the same rate of interest:
⇒ Amount after 30 years = P + (P × R × 30 / 100)
⇒ Amount after 30 years = P + (P × (80 / 3) × 30 / 100)
⇒ Amount after 30 years = P + (P × 800 / 10)
⇒ Amount after 30 years = P + 8P
⇒ Amount after 30 years = 9P
∴ The money becomes 9 times its original value. The correct answer is option 1.
Last updated on May 28, 2025
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