Question

a total of 1400 is invested in two accounts the annual interest rate of one account is 5% and the annual interest rate of the other account is 8% after one year the total amount of interest earned in both accounts is $97 find the amount invested in each of the two accounts

Answer 1

Let's begin by identifying key information given to us:

Principal (2 accounts)= $1,400

Interest Rate (account 1), = 5% = 0.05

Interest Rate (account 2) = 8% = 0.08

Interest (2 accounts) = $97

We will find the amount invested in each account by developing these sets of equations shown below:

`\begin{gathered} x+y=1400---------1 \\ 0.05x+0.08y=97------2 \\ \text{Multiply equation 2 by 100, we have:} \\ 5x+8y=9700--------3 \\ \text{Make ''x'' the subject of equation 1, we have:} \\ x=1400-y \\ \text{Substitute ''x'' into equation 3, we have:} \\ 5(1400-y)+8y=9700 \\ 7000-5y+8y=9700 \\ 7000+3y=9700 \\ \text{Subtract ''7000'' from both sides, we have:} \\ 7000-7000+3y=9700-7000 \\ 3y=2700 \\ \text{Divide both sides by ''3'', we have:} \\ (3)/(3)y=(2700)/(3) \\ y=900 \\ But,x=1400-y \\ x=1400-900=500 \\ x=500 \end{gathered}`

Therefore, the amount of money in the first account is $500 & the amount in the second account is $900