Question

Jody invested $4400 less in account paying 4% simple interest than she did in an account paying 3 percent simple interest. At the end of the first year, the total interest from both accounts was $592. find the amount invested in each account

Answer 1

The rule of the simple interest is

`I=P* R* T`

P is the initial amount

R is the rate in decimal

T is the time

Assume that she invested $x in the account that paid 3% simple interest

then she invested x - 4400 dollars in the account that paid 4% simple interest

Then let us find each interest, then add them, equate the sum by 592

`\begin{gathered} P1=x-4400 \\ R1=(4)/(100)=0.04 \\ T1=1 \\ I1=(x-4400)*0.04*1 \end{gathered}`

Let us simplify it

`\begin{gathered} I1=0.04(x)-0.04(4400) \\ I1=0.04x-176 \end{gathered}`
`\begin{gathered} P2=x \\ R2=(3)/(100)=0.03 \\ T2=1 \\ I2=x*0.03*1 \\ I2=0.03x \end{gathered}`

Since the total interest is $592, then

`\begin{gathered} I1+I2=592 \\ 0.04x-176+0.03x=592 \end{gathered}`

Add the like terms on the left side

`\begin{gathered} (0.04x+0.03x)-176=592 \\ 0.07x-176=592 \end{gathered}`

Add 176 to both sides

`\begin{gathered} 0.07x-176+176=592+176 \\ 0.07x=768 \end{gathered}`

Divide both sides by 0.07 to find x

`\begin{gathered} (0.07x)/(0.07)=(768)/(0.07) \\ x=10971.42857 \end{gathered}`

Then She invested about 10971 dollars in the account of 3%

Since 10971 - 4400 = 6571

Then she invested about