If a loan grew 3 times in 6 years at Simple Interest, then how much time will…

Step-by-Step Solution

To solve this, we need to determine the rate of interest from the first scenario and then apply it to the second scenario.

1. Analyze the first scenario:

   • Let the principal be P.

   • The amount grows 3 times, so the Amount A = 3P.

   • Simple Interest (SI) = Amount - Principal = 3P - P = 2P.

   • Time (T1) = 6 years.

   • Using SI = (P * R * T) / 100:

   • 2P = (P * R * 6) / 100

   • 2 = 6R / 100

   • R = 200 / 6 = 100/3 percent per annum.

2. Analyze the second scenario:

   • We want the loan to grow 8 times, so the Amount A = 8P.

   • Simple Interest (SI) required = 8P - P = 7P.

   • Rate (R) = 100/3 percent.

   • Using SI = (P * R * T) / 100:

   • 7P = (P * (100/3) * T2) / 100

   • 7 = (100 * T2) / (3 * 100)

   • 7 = T2 / 3

   • T2 = 21 years.