Question

Last year, Lucy had $30,000 to invest. She invested some of it in an account that paid 8% simple interest per year, and she invested the rest in an account that paid 6% simple interest per year. After one year, she received a total of $1880 in interest. How much did she invest in each account?

Answer 1

Solution:

Given:

$Pr\text{ incipal= \ 30000}$

Let x be the principal for the 8% simple interest per year

Let y be the principal for the 6% simple interest per year

Hence,

$x+y=30000\ldots\ldots\ldots\ldots\ldots\ldots(1)$

The formula for calculating simple interest is;

$\begin{gathered} I=\frac{P\times T\times R}{100} \\ T=1\text{year} \\ I=\frac{PR}{100} \end{gathered}$$\begin{gathered} I_x=\frac{x\times8}{100} \\ I_x=0.08x \\ \\ I_y=\frac{y\times6}{100} \\ I_y=0.06y \\ \\ I=I_x+I_y=1880 \\ 0.08x+0.06y=1880\ldots\ldots\ldots\ldots\ldots(2) \end{gathered}$

Solving the two equations simultaneously;

$\begin{gathered} x+y=30000\ldots\ldots\ldots\ldots\ldots\ldots(1)\times0.08 \\ 0.08x+0.08y=2400\ldots\ldots\ldots\ldots\ldots\ldots.\text{.}(1) \\ 0.08x+0.06y=1880\ldots\ldots\ldots\ldots\ldots\ldots..(2) \\ \text{Subtracting equation (2) from (1);} \\ \text{equaton (1)-equation (2);} \\ 0.02y=520 \\ \text{Dividing both sides by 0.02 to get y,} \\ y=\frac{520}{0.02} \\ y=26000 \\ \\ \text{Substituting y into equation (1) to get x,} \\ x+y=30000 \\ x+26000=30000 \\ x=30000-26000 \\ x=4000 \end{gathered}$

Therefore,

Lucy invested $4,000 principal for 8% simple interest.

Lucy invested $26,000 principal for 6% simple interest.