A trust fund has invested Rs. 30,000 in two different types of bonds which pays 5% and 7% interest respectively. Determine total interest how much amount is invested in each type of bond if trust obtains an annual of Rs. 1600. (a) Rs.5000 (b) Rs.6000 (c) Rs.7000 (d) Rs. 8000?

Question

Answer

Solution:

Step 1: Formulating the equations

Let the amount invested in the first bond be x, and the amount invested in the second bond be y.

From the given information, we can form two equations:

Equation 1: x + y = 30,000 (Total amount invested)

Equation 2: 0.05x + 0.07y = 1600 (Total annual interest earned)

Step 2: Solving the equations

We can solve the equations simultaneously to find the values of x and y.

Multiplying Equation 1 by 0.05, we get:

0.05x + 0.05y = 1500

Subtracting this equation from Equation 2, we get:

0.02y = 100

y = 5000

Substituting y = 5000 in Equation 1, we get:

x + 5000 = 30,000

x = 25,000

Therefore, Rs. 25,000 is invested in the first bond and Rs. 5,000 is invested in the second bond.

Step 3: Verification

We can verify that the solution is correct by calculating the total annual interest earned:

0.05(25,000) + 0.07(5,000) = 1,250 + 350 = 1,600

Therefore, the total annual interest earned is Rs. 1600.

Answer: (a) Rs.5000

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