On a certain sum, C.I. is Rs 41 and SI is Rs 40. for 2 years. What is the rate p.a.
To find the rate per annum, we can use the formula for compound interest (CI) and simple interest (SI):
Compound Interest (CI) = P * (1 + r/100)^n - P
Simple Interest (SI) = P * r * n / 100
Where:
P = Principal amount (initial sum)
r = Rate of interest per annum
n = Number of years
In this case, we are given:
CI = Rs 41
SI = Rs 40
n = 2 years
We can set up two equations using the above formulas:
Equation 1: CI = P * (1 + r/100)^n - P
41 = P * (1 + r/100)^2 - P
Equation 2: SI = P * r * n / 100
40 = P * r * 2 / 100
We can solve these equations to find the rate per annum (r).
First, let's rearrange Equation 2 to find the Principal amount (P):
40 = P * r * 2 / 100
P = 40 * 100 / (r * 2)
P = 2000 / r
Substituting this value of P into Equation 1:
41 = (2000 / r) * (1 + r/100)^2 - (2000 / r)
Now, we can simplify this equation and solve for r. However, the equation involves a quadratic term [(1 + r/100)^2] which makes solving for r analytically complex.
One way to find an approximate solution is by using numerical methods such as iteration, but it would be quite involved to guide you through that process.
Alternatively, you can use online calculators or spreadsheet software that has built-in functions to solve equations numerically. These tools can provide an accurate estimate for the value of r.
To summarize, to find the rate per annum (r) in this scenario, you can either use numerical methods or utilize online calculators/spreadsheet software to approximate the value.