Question

Lindsey invests $1500 in one account and $900 in an account paying 4 % higher interest. At the end of one year she had earned $204 in interest. At what rates did she invest?

Answer 1

Answer: She invest 41500 at 7% interest and 900 at 11% interest.

Explanation:

Formula for simple interest =
`\frac{\text{Principal x rate x Time}}{100}`

Let
`P_1=\$1500,\ P_2=\$900\ \ \ \ , r_1=r, \ \ r_2=r+4,\ \ \ t_1=t_2=1`

Simple interest by first investment =
`(P_1r_1t_1)/(100)=(1500(r)(1))/(100)=15r`

Simple interest by second investment =
`(P_2r_2t_2)/(100)=(900(r+4)(1))/(100)=9(r+4)`

As per given,

Total interest = $204

`\Rightarrow 15r+9(r+4)=204\\\\\Rightarrow\ 15r+9r+36=204\\\\\Rightarrow\ 24r=204-36\\\\\Rightarrow\ 24r=168\\\\\Rightarrow\ r=(168)/(24)\\\\\Rightarrow\ r=7\%`

Hence, she invest 41500 at 7% interest and 900 at 11% interest.