A trust has Rs 30000 that must be invested in two different types of bonds. The first bond pays 5% interest per year , and second bond pays 7% interest per year . Using matrix multiplication , determine how to divide Rs 30000 among the two bonds . If the trust fund must obtain an annual total interest of 1) Rs 1800 2) 2000
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Let Rs.30,000 be divided into two parts. Assume that the amount invested in the first bond as x, then the amount invested in the second one is Rs(30,000−x). We are given that the first bond pays 5%, i,e., 0.05 in interest and the second bond 7%, i.e., 0.07. We can represent the problem using matrix multiplication as the following 1×2matrix: [x30000−x][0.050.07] which is equal to the interest earned Rs.1800. Given [x30000−x][0.050.07]=1800: [x×(0.05)+(30000−x)×0.07]=1800 0.05x+2100−0.07x=1800 2100−0.02x=1800 2100−1800=0.02x 0.02x=300→x=10.02300 Solving for x x=15,000 and 30,000−x=15,000. Hence the amount has to be divided equally into two sums of Rs.15,000each.
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