A sum of money becomes 3 times itself in 8 years at simple interest. In how many years will it become 5 times itself at the same rate?

Question

Accepted Answer

Simple interest growth is linear and proportional to time.

### Step-by-Step Solution:
1. Let the Principal be $P$.
2. Amount becomes $3P$, which means the Simple Interest ($SI$) earned is:
   $$SI_1 = 3P - P = 2P$$ 
   This happens in $T_1 = 8 	ext{ years}$.
3. We want the amount to become $5P$, which means the required Simple Interest ($SI$) is:
   $$SI_2 = 5P - P = 4P$$ 
   Let the required time be $T_2$.
4. Since Simple Interest is directly proportional to time (at a constant rate):
   $$\frac{SI_1}{SI_2} = \frac{T_1}{T_2}$$
   $$\frac{2P}{4P} = \frac{8}{T_2}$|
   $$\frac{1}{2} = \frac{8}{T_2}$|
   $$T_2 = 8 	imes 2 = 16 	ext{ years}$$

**Answer:** The sum will become 5 times itself in **16 years**.

A sum of money becomes 3 times itself in 8 years at simple interest. In how many years will it become 5 times itself at the same rate? - DDCET Q&A

A sum of money becomes 3 times itself in 8 years at simple interest. In how many years will it become 5 times itself at the same rate?

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