Answer: Option B. -> Rs 6316Given information:
- Amount deposited on compound interest becomes Rs 5700 after three years
- Same amount becomes Rs 6000 after four years
Let's assume that the principal amount is P and the rate of interest is r, compounded annually. Then, we can use the following formula for compound interest:
A = P(1 + r/n)^(nt)
Where,A is the amount after t years,n is the number of times the interest is compounded in a year,t is the time in years,and r is the annual interest rate.
Using this formula, we can form the following equations:
5700 = P(1 + r/1)^(13)6000 = P(1 + r/1)^(14)
Dividing the second equation by the first, we get:
(1 + r)^4 / (1 + r)^3 = 6000/5700
Simplifying, we get:
1 + r = 1.025
r = 0.025
Now, we can use the same formula to find the amount after 5 years:
A = P(1 + r/1)^(1*5)
Substituting the value of r, we get:
A = P(1.025)^5
We don't know the value of P, but we can find it using the information given in the question. If the amount becomes Rs 5700 after 3 years, then the interest earned in the first 3 years is:
I = 5700 - P
Using the formula for compound interest, we can write:
5700 = P(1 + 0.025)^3P = 5700 / 1.025^3
Similarly, if the amount becomes Rs 6000 after 4 years, then the interest earned in the first 4 years is:
I = 6000 - P
Using the formula for compound interest, we can write:
6000 = P(1 + 0.025)^4P = 6000 / 1.025^4
We can equate these two values of P and solve for I:
5700 / 1.025^3 = 6000 / 1.025^4
I = 183.28
So, the principal amount is:
P = 5700 - 183.28 = 5516.72
Now, we can use this value of P to find the amount after 5 years:
A = 5516.72(1.025)^5 = 6316.10
Therefore, the correct answer is option B, Rs 6316.If you think the solution is wrong then please provide your own solution below in the comments section .
