A sum of money invested at compound interest amounts to Rs.4,624 in 2 years and to Rs.4,913 in 3 years. The sum of money is:
800
To find the principal sum of money invested, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount
P is the principal amount
r is the annual interest rate
n is the number of times interest is compounded per year
t is the number of years
Let's use the given information to solve the problem:
First, we'll find the interest rate (r/n) using the given data for 2 and 3 years:
A1 = Rs.4,624 (amount after 2 years)
A2 = Rs.4,913 (amount after 3 years)
Now, we can set up the following equations:
A1 = P(1 + r/n)^(nt1)
A2 = P(1 + r/n)^(nt2)
Dividing the second equation by the first equation, we get:
A2/A1 = [P(1 + r/n)^(nt2)] / [P(1 + r/n)^(nt1)]
Simplifying this equation, we can cancel out the P terms:
A2/A1 = (1 + r/n)^(nt2 - nt1)
Substituting the given values:
4913/4624 = (1 + r/n)^(3-2)
Doing the math:
4913/4624 = (1 + r/n)
Now, we have an equation to find (1 + r/n). Let's solve for it:
(1 + r/n) = 4913/4624
(1 + r/n) ≈ 1.0619
Now, we can plug this value back into one of the original equations to find P, the principal sum of money:
A1 = P(1 + r/n)^(nt1)
4624 = P(1.0619)^2
Now, solve for P:
P ≈ 4624 / (1.0619)^2
P ≈ 4320.48
Therefore, the principal sum of money invested is approximately Rs. 4,320.48.