Sure, let's start solving the problem step by step.
Firstly, let's find out the rate of interest. We know the initial amount, the final amount after 2 years, and we want to know the rate of interest. By using the simple interest formula, we have:
final_amount1 = initial_amount1 * (1 + (rate_of_interest * years1)),
where final_amount1 is the amount after 2 years, which is Rs.4560, initial_amount1 is the initial amount which is Rs.4000, years1 is the time span, which is 2 years, and rate_of_interest is what we need to estimate.
By rearranging this formula, we can solve for the rate of interest, our formula is now:
rate_of_interest = (final_amount1 - initial_amount1) / (initial_amount1 * years1),
Which gives:
rate_of_interest = (4560 - 4000) / (4000 * 2)
If you plug the values in and evaluate the expression, you will get:
rate_of_interest = 0.07.
This means, the rate of interest is 7%.
Now that we know the rate of interest, we can calculate the amount of Rs.5000 at the end of 4 years with the same rate of interest.
We use the same formula rearranged for the final_amount:
final_amount2 = initial_amount2 * (1 + (rate_of_interest * years2)),
where initial_amount2 is Rs.5000 and years2 is 4 years.
Plugging in these values:
final_amount2 = 5000 * (1 + (0.07 * 4))
Evaluating this,
final_amount2 = 6400.0.
So, Rs.5000 will amount to Rs.6400 at the end of 4 years.
In conclusion, considering the given initial and final amounts, the rate of interest is 7%. Therefore, Rs.5000 will become Rs.6400 in 4 years with the same rate of interest under simple interest.
Answer: Rs. 5000 will amount to Rs.6400 at the end of 4 years