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. 2000

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.2000Rs.2000.

Given [x30000−x][0.050.07]=2000[x30000−x][0.050.07]=2000:

[x×(0.05)+(30000−x)×0.07]=2000[x×(0.05)+(30000−x)×0.07]=2000

0.05x+2100−0.07x=20000.05x+2100−0.07x=2000

2100−0.02x=20002100−0.02x=2000

2100−2000=0.02x2100−2000=0.02x

0.02x=100→x=10.021000.02x=100→x=10.02100

Solving for xx, x=5,000x=5,000 and 30,000−x=25,00030,000−x=25,000.

Hence the amount has to be divided into two sums of Rs.5,000Rs.5,000 and Rs.25,000Rs.25,000.