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A trust fund has 30,000 that must be invested in two different types of bonds. The first bond pays 5% interest per year, and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide 30,000 among the two: (i) Rs. 1800

Q19.    A trust fund has Rs. 30,000 that must be invested in two different types of bonds. The first bond pays 5% interest per year, and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide Rs 30,000 among the two types of bonds. If the trust fund must obtain an annual total interest of:

 (a) Rs. 1800

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Let Rs. x be invested in the first bond.

Money invested in second bond = Rs (3000-x)

The first bond pays 5% interest per year and the second bond pays 7% interest per year.

To obtain an annual total interest of  Rs. 1800,  we have

\begin{bmatrix}x &(30000-x) \end{bmatrix} \begin{bmatrix} \frac{5}{100} \\ \frac{7}{100} \end{bmatrix}  =1800                       (simple interest for 1 year =\frac{pricipal\times rate}{100} )

\frac{5}{100}x+\frac{7}{100}(30000-x) = 1800

5x+210000-7x=180000

210000-180000=7x-5x

 30000=2x

x=15000

Thus, to obtain an annual total interest of  Rs. 1800, the trust fund should invest Rs 15000 in the first bond and Rs 15000 in the second bond.

 

 

 

 

 

 

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