If a loan grew 3 times in 6 years at Simple Interest, then how much time will it take to grow 8 times?

Correct option is D

Given:

Let the principal (initial loan amount) be denoted as ( P ).
If the loan grows 3 times in 6 years, the total amount after 6 years is ( 3P ), and the interest earned is ( 2P).

Concept Used:
The formula for Simple Interest (SI) is given by:
​$$SI = \frac{P \times R \times T}{100}$$​​
where (P) is the principal, (R) is the rate of interest per annum, and (T) is the time in years.
From the information given, (2P) is the interest for 6 years. Using the Simple Interest formula:
​$$2P = \frac{P \times R \times 6}{100}$$​​
​$$R = \frac{2P \times 100}{P \times 6} = \frac{200}{6} = 33.33\%$$​​
Now, to grow the loan 8 times, the total amount will be ( 8P ), so the interest earned will be ( 7P ).
We will use the same Simple Interest formula to find the time (T):
​$$7P = \frac{P \times 33.33 \times T}{100}$$​​
​$$T = \frac{7P \times 100}{P \times 33.33} = \frac{700}{33.33} \approx 21\text{ years}$$​​
The loan will take approximately 21 years to grow 8 times.