Question

Suppose $1,000 is divided into two bank accounts. One account pays 1% simple interest per year and the other pays 2.5%. After three years there is a total of $55 in interest between the two accounts. How much was invested into the bank account that pays 1% simple interest (rounded to the nearest cent)?
Please explain aswell.

Answer 1

Call the 1% account X
After 3 years the interest it earned is X times 1% for 3 years
=X(.01)(3)
=0.03X

The 2.5% account has (1000 - X) dollars
It earns (1000-X(.025)(3)
=(1000 - X)(.075)
=75-.075X
The total of the interest is 55
Therefore .03X + 75 -.075X = 55
- .045X = 55 - 75
-.045X = -20
.045X = 20
45X =20000
X = 20000 / 45
X = $ 444.44

Therefore the amount invested id the 2.5% account is
1000 - 444.44
=$ 555.56