Question

b) Madan Bahadur deposited a sum of money at his bank account at the rate of 10% p.a.. After 5 years, he received Rs 1900, the net interest when 5% of the total interest was charged as income tax. Find, how much sum was deposited by him?​

Answer 1

To find the sum deposited by Madan Bahadur, use the compound interest formula and solve for the principal. Then, substitute the value of the total interest into the equation to find the principal. Finally, determine the principal amount by trial and error or using a financial calculator or software.

Step-by-step explanation:

To find the sum deposited by Madan Bahadur, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where A is the final amount, P is the principal, r is the annual interest rate in decimal form, n is the number of times interest is compounded per year, and t is the number of years.

In this case, we have:

Rs 1900 = P(1 + 0.1/n)^(n * 5)

From the given information, we know that 5% of the total interest was charged as income tax. This means that Madan Bahadur received 95% of the total interest, or 0.95 times the total interest.

So, 0.95 * Total Interest = Rs 1900

Let's call the total interest I:

0.95I = Rs 1900

I = Rs 1900 / 0.95

Now, we can substitute the value of I into the compound interest formula:

P(1 + 0.1/n)^(n * 5) = I

P(1 + 0.1/n)^(n * 5) = Rs 1900 / 0.95

From here, we can solve for P by trial and error or by using a financial calculator or software.