Solution:

Calculating the Equal Annual Instalment:

To calculate the equal annual instalment, we need to use the formula:

E = P x r x (1 + r)^n / ((1 + r)^n - 1)

where,
E = Equal annual instalment
P = Principal amount borrowed
r = Rate of interest per annum
n = Total number of years for repayment

Given that,
P = Rs.50,00,000
r = 10% per annum
n = 20 years

Substituting these values in the formula, we get:

E = 50,00,000 x 0.10 x (1 + 0.10)^20 / ((1 + 0.10)^20 - 1)

E = Rs.6,07,986 (approx.)

Therefore, the equal annual instalment that Shoba needs to pay for 20 years to repay the loan of Rs.50,00,000 with 10% interest on the outstanding balance is Rs.6,07,986 (approx.).

Understanding the Calculation:

To understand this calculation in detail, let us break down the formula for equal annual instalment:

E = P x r x (1 + r)^n / ((1 + r)^n - 1)

1. Calculation of (1 + r)^n:
The first step is to calculate (1 + r)^n, which represents the compound interest factor for n years. In this case, n = 20 and r = 10% per annum. Therefore,

(1 + r)^n = (1 + 0.10)^20 = 6.7275 (approx.)

2. Calculation of the denominator ((1 + r)^n - 1):
The denominator of the formula is ((1 + r)^n - 1), which represents the discount factor. In this case, we have already calculated (1 + r)^n, which is 6.7275 (approx.). Therefore,

((1 + r)^n - 1) = (6.7275 - 1) = 5.7275 (approx.)

3. Calculation of the numerator (P x r x (1 + r)^n):
The numerator of the formula is P x r x (1 + r)^n, which represents the interest component of the instalment. In this case, P = Rs.50,00,000 and r = 10% per annum. Therefore,

P x r x (1 + r)^n = 50,00,000 x 0.10 x 6.7275 = Rs.33,63,750 (approx.)

4. Calculation of the equal annual instalment (E):
Finally, we can calculate the equal annual instalment (E) by dividing the numerator (P x r x (1 + r)^n) by the denominator ((1 + r)^n - 1). Therefore,

E = P x r x (1 + r)^n / ((1 + r)^n - 1) = 33,63,750 / 5.7275 = Rs.6,07,986 (approx.)

Conclusion:

Hence, we can conclude that Shoba needs to pay Rs.6,07,986 (approx.) as an equal annual instalment for 20 years to repay the loan of Rs.50,00,000 with 10% interest on