Aman invests ₹4000 in a bank at a certain rate of interest, compounded annually. If the ratio of the value of the investment after 3 years to the value of the investment after 5 years is 25:36, then the minimum number of years required for the value of the investment to exceed ₹20000 is:

Question

Accepted Answer

1. **Determine the Rate of Interest:**  
   - The formula for compound interest is:  
     $$
     P 	imes \left(1 + \frac{r}{100}ight)^n
     $$  
   - Given ratio:  
     $$
     \frac{4000 	imes \left(1 + \frac{r}{100}ight)^3}{4000 	imes \left(1 + \frac{r}{100}ight)^5} = \frac{25}{36}
     $$  
   - Simplify:  
     $$
     \left(1 + \frac{r}{100}ight)^2 = \frac{36}{25}
     $$  
   - Solve for $$ r $$:  
     $$
     1 + \frac{r}{100} = \sqrt{\frac{36}{25}} = \frac{6}{5}
     $$  
     $$
     r = 20\%
     $$

2. **Calculate Minimum Years to Exceed ₹20000:**  
   - Use compound interest formula:  
     $$
     4000 	imes \left(1 + 0.2ight)^n > 20000
     $$  
   - Simplify:  
     $$
     (1.2)^n > 5
     $$  
   - Solve using logarithms or approximation:  
     $$ n = 9$$.

Thus, the minimum number of years required for the investment to exceed ₹20000 is **9 years**.