Solution:

To find the amount of loan taken by Abdul, we need to use the formula for calculating the present value of an annuity.

An annuity is a series of equal payments made at regular intervals. In this case, Abdul has to make three equal payments of Rs. 10,000 each.

Formula to calculate the present value of an annuity:

PV = A * [(1 - (1 + r)^-n) / r]

Where,
PV = Present value of the annuity
A = Amount of each payment
r = Interest rate per period
n = Number of periods

Here, A = Rs. 10,000, r = 7% per annum, and n = 3 (since there are three equal payments).

Step-by-step calculation:

1. Convert the annual interest rate to a monthly rate by dividing it by 12.
Monthly interest rate = 7% / 12 = 0.5833%

2. Calculate the present value of each payment using the formula:
PV = A / (1 + r)^t
where t is the number of periods (in months)

PV1 = 10,000 / (1 + 0.5833%)^1 = Rs. 9,934.58
PV2 = 10,000 / (1 + 0.5833%)^2 = Rs. 9,871.12
PV3 = 10,000 / (1 + 0.5833%)^3 = Rs. 9,807.63

3. Calculate the total present value of the annuity by adding the present values of each payment.

Total PV = PV1 + PV2 + PV3
= Rs. 29,613.33

Therefore, the amount of loan taken by Abdul from Bahadur is Rs. 29,613.33.

Explanation:

Abdul has taken a loan from Bahadur at 7% per annum, which means he has to pay an interest rate of 7% on the loan amount. The loan has to be repaid in three equal installments of Rs. 10,000 each. To calculate the amount of loan taken, we need to find the present value of the annuity, which is the total amount that Abdul would need to repay to Bahadur to settle the loan.

We use the formula for present value of an annuity, which takes into account the amount of each payment, the interest rate per period, and the number of periods. By calculating the present value of each payment and adding them up, we get the total present value of the annuity, which is the amount of loan taken by Abdul.

It is important to note that the interest rate used in the calculation is the monthly interest rate, which is derived from the annual interest rate by dividing it by 12. This is because the payments are made monthly, and the interest is compounded monthly.

P.V/A.R = P((1+i)^n-1)÷i(1+i)^n

Loan = 10000 ((1.07)^3-1)÷.07(1.07)^3
= 10000×0.225043÷.80543
= 26243(App....)