a sum of money borrowed at a particular rate of interest amounts to Rs 8320 in 2 years and Rs 9685 in 7/2 years. Find the sum borrowed.
amount borrowed ---- x
rate of interest ---- i
x(1+i)^2 = 8320
x(1+i)^3.5 = 9685
divide the second equation by the first:
(1+i)^1.5 = 1.1640625
(1+i)^(3/2) = 1.1640625
1+i = 1.1640625^(2/3) = 1.10658
i = .10658
plug your value into the first equation, let me know what you get.
A sum of money borrowed at a particular rate of interest amount to Rs 8320 in 2 years and Rs 9685 7/2 years. Find the sum borrowed
To find the sum borrowed, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the total amount after time t
P = principal (sum borrowed)
r = rate of interest
n = number of times interest is compounded per year
t = time in years
Let's solve this step by step:
Step 1:
From the given information, we have:
A1 = Rs 8320
t1 = 2 years
Step 2:
Substituting the values in the formula, we have:
8320 = P(1 + r/n)^(nt1)
Step 3:
Next, let's consider the second set of information:
A2 = Rs 9685
t2 = 7/2 years
Step 4:
Substituting these values in the formula, we have:
9685 = P(1 + r/n)^(nt2)
Step 5:
Now, we have two equations with two unknowns (P and r). We can solve them simultaneously to find the values of P and r.
From the equation in step 2:
8320 = P(1 + r/n)^(2n)
From the equation in step 4:
9685 = P(1 + r/n)^(7/2n)
Step 6:
To simplify the calculations, let's choose values for n that will make the equation easier. For example, if we choose n = 2, the first equation will become:
8320 = P(1 + r/2)^(4)
And the second equation will become:
9685 = P(1 + r/2)^(7)
Step 7:
Now, we can use these equations to solve for P and r. We can use algebraic methods or trial and error to find the values.
Step 8:
Once you have found the values of P and r, you will have the answer to your question, which is the sum borrowed.