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.

Step-by-step explanation:

Formula for simple interest = $\dfrac{\text{Principal x rate x Time}}{100}$

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

Simple interest by first investment = $\dfrac{P_1r_1t_1}{100}=\dfrac{1500(r)(1)}{100}=15r$

Simple interest by second investment = $\dfrac{P_2r_2t_2}{100}=\dfrac{900(r+4)(1)}{100}=9(r+4)$

As per given,

Total interest = $204

$\Rightarrow 15r+9(r+4)=204\\\\\Rightarrow\ 15r+9r+36=204\\\\\Rightarrow\ 24r=204-36\\\\\Rightarrow\ 24r=168\\\\\Rightarrow\ r=\dfrac{168}{24}\\\\\Rightarrow\ r=7\%$

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