Question

Last year, Debra had $10,000 to invest. She invested some of it in an account that paid 6% simple interest per year, and she invested the rest in an accountthat paid 8% simple interest per year. After one year, she received a total of $720 in interest. How much did she invest in each account?

Answer 1

Given :

Amount to be invested = $ 10,000

rate of first account = 6%

rate of second account = 8%

Total amount she received on interest = $720

Solution

Let the amount she invested in the first account be x

Let the amount she invested in the second account be y

Then,

$x\text{ + y = 10 000}$

Also, using the simple interest formula:

$S\mathrm{}I\text{ = }\frac{P\times R\times T}{100}$

We can express the second and last statements mathematically

$\begin{gathered} \frac{x\text{ }\times\text{ 6}\times1}{100}\text{ + }\frac{y\text{ }\times\text{ 8 }\times\text{ 1}}{100}\text{ = 720} \\ re-\text{arranging} \\ 6x\text{ + 8y = 72000} \end{gathered}$

We can solve the equations simultaneously to obtain x and y

$\begin{gathered} x\text{ + y = 10000} \\ 6x\text{ + 8y = 72000} \\ x\text{ = 4000} \\ y\text{ = 6000} \end{gathered}$

She invested $4000 and $6000 respectively.