On a certain sum, Compound interest is Rs41 and Simple interest is Rs 40. for 2 years. What is the rate p.a.?
Initial sum = S
Interest rate = r
S*2r = 40
S*r + S*(1+r)*r = 41
S*2r + S*r^2 = 41
S*r^2 = 1
2/r = 40
r = 1/20 = 5% is the rate per annum.
S = 400 is the initial sum (rupees)
Thank you drwls ,
To find the rate per annum (p.a.), we can use the formulas for compound interest (CI) and simple interest (SI).
The formula for compound interest is: CI = P(1 + r/n)^(n*t) - P
where:
- CI is the compound interest
- P is the principal sum (the initial amount)
- r is the rate of interest (in decimal form)
- n is the number of times interest is compounded per year
- t is the number of years
The formula for simple interest is: SI = P * r * t
where:
- SI is the simple interest
Given that the compound interest is Rs 41 and the simple interest is Rs 40 for 2 years, we can set up the following equations:
Equation 1: CI = P(1 + r/n)^(n*t) - P = 41
Equation 2: SI = P * r * t = 40
Now, we need to solve these equations to find the rate of interest (r).
Let's start with Equation 2:
SI = P * r * t
Since SI = 40 and t = 2, we can rewrite the equation as:
40 = P * r * 2
Dividing both sides of the equation by P * 2, we get:
r = 40 / (P * 2)
Now, substitute this value of r into Equation 1:
41 = P(1 + r/n)^(n*t) - P
Replacing r with 40 / (P * 2):
41 = P(1 + 40 / (P * 2) /n)^(n*t) - P
Simplifying this equation may require some additional information, such as the value of n (the number of times interest is compounded per year). Without that information, we cannot proceed further to find the rate per annum (p.a.).