Question

Ms. Jamison plans to invest $3,800 in two accounts for one year. The first account earns a yearly interest of 3.5%. The second account earns a yearly interest of 6%. How much money does Ms. Jamison need to invest in the second account in order to earn $188 in interest from both accounts? Show all of your work.

Answer 1

The Amount investment in second account is $2200

Explanation:

Given as :

Total money invested in two accounts = $3800

The time period of investment = t = 1 year

Let The amount investment in first account = $p

Let The amount investment in second account = $3800 - $p

The rate of interest for first account =
`r_1` = 3.5%

The rate of interest for second account =
`r_2` = 6%

The total interest earn from both account = s.i = $188

Let The interest earn from first account =
`s.i_1`

Let The interest earn from second account =
`s.i_2`

Now, From simple interest method

Simple interest =
`(\textrm principal* \textrm rate* \texrm time)/(100)`

For First account

`s.i_1` =
`(p* r_1* t)/(100)`

i.e
`s.i_1` =
`(p* 3.5* 1)/(100)`

Again

For second account

`s.i_2` =
`((3800-p)* r_2* t)/(100)`

`s.i_2` =
`((3800-p)* 6* 1)/(100)`

Since total interest earn from both account = s.i = $188

i.e s.i =
`s.i_2` +
`s.i_2`

Or, s.i =
`(p* 3.5* 1)/(100)` +
`((3800-p)* 6* 1)/(100)`

Or, $188 =
`(p* 3.5* 1)/(100)` +
`((3800-p)* 6* 1)/(100)`

Or, 188 × 100 = 3.5 p + 22800 - 6 p

Or, 6 p - 3.5 p = 22800 - 18800

Or, 2.5 p = 4000

∴ p =
`(4000)/(2.5)`

i.e p = $1600

So, The amount investment in first account = p = $1600

So, The amount investment in second account = $3800 - $p

i.e The amount investment in second account = $3800 - $1600

Or, The amount investment in second account = $2200

Hence, The Amount investment in second account is $2200 Answer