The loan of RS 10000 is to be paid back in 30 equal installments .the amt. Of each installment to cover the principal and at 4% p.a. CI is???? Ans is 578.87. Explain this ans ?

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Calculation of Total Payment

The first step in finding the amount of each installment is to calculate the total payment that has to be made by the borrower.

Total Payment = Principal + Interest

Here, the principal is Rs. 10,000, and the interest is to be calculated at a rate of 4% p.a. compounded annually.

Using the formula for compound interest, we can find the total payment as follows:

A = P * (1 + r/n)^(n*t)

where

A = total amount after t years
P = principal amount
r = annual interest rate
n = number of times the interest is compounded per year
t = time in years

In this case,

P = Rs. 10,000
r = 4% p.a.
n = 1 (as interest is compounded annually)
t = 30/12 = 2.5 years (as the loan is to be repaid in 30 equal installments)

Substituting these values, we get:

A = 10000 * (1 + 0.04/1)^(1*2.5)
= 10000 * (1.04)^2.5
= 10000 * 1.1155
= Rs. 11,155

Therefore, the total payment that has to be made by the borrower over the period of the loan is Rs. 11,155.

Calculation of Installment Amount

Now, we can find the amount of each installment by dividing the total payment by the number of installments.

Installment Amount = Total Payment / Number of Installments

Here, the number of installments is 30, as the loan is to be repaid in 30 equal installments.

Substituting the values, we get:

Installment Amount = 11155 / 30
= Rs. 371.83 (rounded off to two decimal places)

However, this installment amount only covers the principal amount. We need to add the interest component to this amount to get the actual installment amount.

Calculation of Interest Component

The interest component for each installment can be found by using the formula for compound interest as follows:

A = P * (1 + r/n)^(n*t)

where

A = total amount after t years
P = principal amount
r = annual interest rate
n = number of times the interest is compounded per year
t = time in years

In this case,

P = Rs. 10,000
r = 4% p.a.
n = 1 (as interest is compounded annually)
t = 1/30 = 0.0333 years (as each installment covers a period of 1 month, which is 1/30th of a year)

Substituting these values, we get:

A = 10000 * (1 + 0.04/1)^(1*0.0333)
= 10000 * 1.0013
= Rs. 10013

Therefore, the interest component for each installment is Rs. (10013 - 10000) = Rs. 13.

Calculation of Actual Installment Amount

Finally, we can add the principal and interest components to get the actual installment amount.

Actual Installment Amount = Installment Amount + Interest Component

Sub

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Under the Rural Housing Scheme, the Delhi Development Authority (DD

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