Chapter 6.4, Problem 9PPE

To determine

To calculate: Amount invested in each account.

Answer to Problem 9PPE

Amount invested in account $A$ is $\$950$ and $B$ is $\$550$

Explanation of Solution

Given information: You split $\$1500$ between two savings accounts. Account $A$ pays annual $5\%$ interest and Account $B$ pays $4\%$ annual interest. After one year, you have earned a total of $\$69.50$ in interest.

Calculation:

Let’s assume $\$x$ is invested in account $A$ and $\$y$ is invested in account $B$

Now, the total money invested is, $x+y=\$1500$.......(i)

The annual interest on account $A$ is given by, $\frac{5x}{100}$

  $(I=\frac{PRN}{100})$

The annual interest on account $B$ is given by, $\frac{4y}{100}$

Now, the total earned interest is, $\frac{5x}{100}+\frac{4y}{100}=69.50$ , $\therefore 5x+4y=6950$......(ii)

Now, substitute value of $y$ from the equation (i) to (ii),

  $\therefore 5x+4(1500-x)=6950$

  $\therefore x=950$

Substitute value of $x$ into equation (i), $\therefore y=1500-950=550$

Therefore, amount invested in account $A$ is $\$950$ and $B$ is $\$550$