Question

Ms. Hagan invested twice as much money in an account that pays 7% interest as she did in an account that pays 6% in interest. Her total investment pays her $1,000 a year in interest. How much did she invest at each rate?

Answer 1

Answer: She invested $5000 in an account that pays 6% interest and $10000 in an account that pays 7% interest.

Step-by-step explanation:

Let P be the initial amount she invested in an account that pays 6% interest.

Then, amount invested in other account = 2P

Simple interest = Principal x rate x time

After one year, for the first account,

Interest = P(0.06)(1)  = 0.06P

For second account,

Interest = (2P)(0.07)(1)=0.14P

Total interest = $0.06P+0.14P=1000$

$\Rightarrow\ 0.20P=1000\\\\\Rightarrow\ P=\dfrac{1000}{0.20}\\\\\Rightarrow\ P=5000$

2P = 2(5000)=10000

Hence, She invested $5000 in an account that pays 6% interest and $10000 in an account that pays 7% interest.