Question

A trust fund has Rs. 30,000 that must be invested in two different type of bounds the fist bond pays 5% interest per year and the second bond pays 7% interest per yer using matrix multiplication determine how to divide Rs.30,000 among the two type of bound if the trust fund must obtain an annual total interest of
a)Rs.1800

Answer 1

Let Rs.30,000Rs.30,000 be divided into two parts. Assume that the amount invested in the first bond as xx, then the amount invested in the second one is Rs(30,000−x)Rs(30,000−x).

We are given that the first bond pays 5%5%, i,e., 0.050.05 in interest and the second bond 7%7%, i.e., 0.070.07.

We can represent the problem using matrix multiplication as the following 1×21×2 matrix: [x30000−x][0.050.07][x30000−x][0.050.07]which is equal to the interest earned Rs.1800Rs.1800.

Given [x30000−x][0.050.07]=1800[x30000−x][0.050.07]=1800:

[x×(0.05)+(30000−x)×0.07]=1800[x×(0.05)+(30000−x)×0.07]=1800

0.05x+2100−0.07x=18000.05x+2100−0.07x=1800

2100−0.02x=18002100−0.02x=1800

2100−1800=0.02x2100−1800=0.02x

0.02x=300→x=10.023000.02x=300→x=10.02300

Solving for xx, x=15,000x=15,000 and 30,000−x=15,00030,000−x=15,000.

Hence the amount has to be divided equally into two sums of Rs.15,000Rs.15,000 each.