Question

Ms wash investdd $22000 in two accounts, one yielding 8% interest and the other yielding 11%. if she recieved a total of $1910 in interest at the end of the year, how much did she invest in each accouny

Answer 1

Take into account the following formula for the simple interest:

`I=P\cdot r\cdot t`

where:

P: principal investment

r: interest rate

t: time

In order to determine the investments for both accounts, proceed as follow:

-Consider that both investments are represented by P1 and P2 respectively, then, you have:

`\begin{gathered} P_1+P_2=22000 \\ P_2=22000-P_1 \end{gathered}`

- Next, use the given values for parameters r and t for each investment:

8% = 0.08

11% = 0.11

t = 1 year

`\begin{gathered} I_1=P_1\cdot0.08\cdot1=0.08P_1 \\ I_2=P_2\cdot0.11\cdot1=0.11P_2 \end{gathered}`

- Next, consider that the sum of the total earnings is $1910, then:

`I_1+I_2=1910`

- Replace I1 and I2 by the expressions in terms of P1 and P2 and write down the resultant expression in terms of P1, as follow:

`\begin{gathered} 0.08P_1+0.11P_2=1910 \\ 0.08P_1+0.11(22000-P_1)=1910 \\ 0.08P_1+2420-0.11P_1=1910 \\ -0.03P_1=-510 \\ P_1=(510)/(0.03)=17000 \end{gathered}`

And for P2:

`\begin{gathered} P_2=22000-P_1 \\ P_2=22000-17000=5000 \end{gathered}`

Hence, the amount of money invested in each account was $5000 and $17000