Question

A total amount of Rs. 7,000 is deposited in three different savings bank accounts with annual interest rates of 5%, 8% and 8 $\frac{1}{2}$ % respectively. The total annual interest from these three accounts is Rs. 550. Equal amounts have been deposited in the 5% and 8% savings accounts. Find the amount deposited in each of the three accounts, with the help of matrices.

Answer 1

Let $x,y,z$ be the amounts deposited in different savings accounts
$x$ in 5% savings account,$y$ in 8% savings account,$z$ in 8.5% savings account
$x+y+z=7000$
$5x+8y+8.5z=55000$
given that $x=y$
writing above linear equations in matrix form
$\left[\begin{array}{cc}2& 1\\ 26& 17\end{array}\right]\left[\begin{array}{c}x\\ z\end{array}\right]=\left[\begin{array}{c}7000\\ 110000\end{array}\right]\left[\begin{array}{c}x\\ z\end{array}\right]=\frac{1}{8}\left[\begin{array}{cc}17& -1\\ -26& 2\end{array}\right]\left[\begin{array}{c}7000\\ 110000\end{array}\right]\left[\begin{array}{c}x\\ z\end{array}\right]=\left[\begin{array}{c}1125\\ 4750\end{array}\right]$
Hence amounts deposited in different accounts are 1125, 1125, 4750.