What sum (in Rs) given on loan for two years with scheme of return on the basis of compound interest at a yearly rate of 10% will correspond to repayment through equal monthly installments of Rs.9075?

To solve this problem, we need to use the formula for the present value of an annuity because the loan is being repaid in equal monthly installments. The formula is:

P = PMT * [(1 - (1 + r/n) ^ -nt) / (r/n)]

Where: P = present value, or the amount of the loan PMT = amount of each payment, or Rs.9075 r = annual interest rate, or 10% = 0.10 n = number of times the interest is compounded per year, or 12 (monthly) t = number of years, or 2

First, we need to convert the annual interest rate to a monthly rate by dividing by 12:

r/n = 0.10 / 12 = 0.008333

Then, we can substitute the values into the formula:

P = 9075 * [(1 - (1 + 0.008333) ^ -24) / 0.008333]

Solving the equation inside the brackets first:

(1 + 0.008333) ^ -24 = 0.83526

Subtracting this from 1:

1 - 0.83526 = 0.16474

Then, dividing by the monthly interest rate:

0.16474 / 0.008333 = 19.77

Finally, multiplying by the monthly payment amount:

9075 * 19.77 = Rs.179,307.75

So, the sum given on loan would be approximately Rs.179,307.75.