a certain sum of money atcompound interest becomes Rs7396 in 2 years and Rs7950.70 in 3 years.Find the rate of interest
let the amount be A
and the annual rate of interest i
then:
A(1+i)^3 = 7950 , #1
and
A(1+i)^2 = 7396 , #2
divide #1 by #2
1+i = 1.0749
i = .0749 or 7.49 %
Macho bhenchho
To find the rate of interest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Total amount after interest
P = Principal amount (initial sum of money)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Time in years
In this case, we have two equations:
1) A = P(1 + r/n)^(nt), with A = Rs7396, P (Principal) = ? , r (rate of interest) = ?, n = ? , and t = 2
2) A = P(1 + r/n)^(nt), with A = Rs7950.70, P (Principal) = ? , r (rate of interest) = ?, n = ? , and t = 3
In order to solve for the rate of interest, we need to find the values of P, n, and solve the system of equations.
To eliminate P and n from the equations, we can take the ratio of the two equations:
(Rs7396) / (Rs7950.70) = (P(1 + r/n)^(nt)) / (P(1 + r/n)^(3n))
Simplifying:
(7396) / (7950.70) = (1 + r/n)^(2n) / (1 + r/n)^(3n)
Now, simplify the left side:
0.9291 = (1 + r/n)^(-n)
Taking the reciprocal:
(1 + r/n)^n = 1 / 0.9291
Taking the nth root:
1 + r/n = (1 / 0.9291)^(1/n)
Now, let's assume a value for 'n' (compounding frequency per year) - usually given as either 1, 2, 4, or 12 (for annual, semi-annual, quarterly, or monthly compounding respectively). Let's choose n = 1 (annual compounding) for now:
1 + r/1 = (1 / 0.9291)^(1/1)
Solving for r:
1 + r = 1.074770
r = 1.074770 - 1
r = 0.074770
So, the rate of interest (annual percentage) is approximately 7.477%, assuming compounding is done annually.