A sum of money borrowed at a particular rate of interest amounts of Rs 8320 in 2years and Rs 9685 in 3 and half years.Find the sum borrowed.
a(1+2r) = 8320
a(1+3.5r) = 9685
a = 6500
6500
To find the sum borrowed, we can start by representing the information given.
Let's denote the sum borrowed as 'P' and the rate of interest as 'R'.
From the information provided, we know that the sum borrowed amounts to Rs 8320 in 2 years and Rs 9685 in 3 and a half years.
Using the formula for compound interest, we can calculate the sum borrowed. The formula for compound interest is:
A = P(1 + R/100)^t
Where:
A is the final amount
P is the principal amount (the sum borrowed)
R is the rate of interest
t is the time period in years
For the first case where the sum borrowed amounts to Rs 8320 in 2 years:
8320 = P(1 + R/100)^2
For the second case where the sum borrowed amounts to Rs 9685 in 3.5 years:
9685 = P(1 + R/100)^(7/2)
These are two equations with two unknowns (P and R). We can solve them using simultaneous equations.
First, let's simplify the second equation by taking the square root:
√(9685) = √(P(1 + R/100)^(7/2))
97.92 = √(P(1 + R/100)^3.5)
Now we can rearrange the equation to isolate P:
P(1 + R/100)^3.5 = (97.92)^2
P(1 + R/100)^3.5 = 9587.3664
Next, we can substitute the value of P from the first equation into the second equation:
8320(1 + R/100)^3.5 = 9587.3664
Now, we can solve this equation for the rate of interest 'R'.
After calculating 'R', we can substitute the value of 'R' back into the first equation to find the sum borrowed 'P'.
Please note that this calculation may require using trial and error or numerical methods, such as graphing or using a calculator, to approximate the value of 'R'.