Question

A principal amount of Rs 40000 becomes Rs 62500 in one year if the interest is compounded semi-annually at a certain rate. If the principal is( 1)/(4) th of the principal amount, what will be the annual compound interest at( 1)/(5) th of the 2-year interest rate?

Answer 1

To find the annual compound interest, we need to determine the interest rate, and use it to calculate the compound interest. The interest rate can be found by using the compounding formula. Then, we can find the annual compound interest by multiplying the 2-year interest rate by 1/5.

Step-by-step explanation:

Let's break down the problem step by step to find the annual compound interest.

Given that the principal amount is Rs 40000 and it becomes Rs 62500 in one year, we need to determine the interest rate and use it to calculate the compound interest.

First, let's find the interest rate. To do this, we can use the compounding formula: Total amount = Principal *(1 + Interest rate/100) ^ n, where n is the number of compounding periods.

In this case, since the interest is compounded semi-annually, we have 2 compounding periods in a year. Therefore, 62500 = 40000 * (1 + Interest rate/100 )^2.

Simplifying the equation, we get (1 + Interest rate/100 )^2 = 62500/40000. Taking the square root of both sides, we get (1 + Interest rate/100) = sqrt(62500/40000).

Now, let's find the annual compound interest at 1/5th of the 2-year interest rate. Since we know the 2-year interest rate, we can multiply it by 1/5 to find the annual compound interest. Let's call the 2-year interest rate R. The annual compound interest would then be R*(1/5).