Question

Laura bought a 5 year treasury note that paid 2.8% simple interest. She invested $5000 more in a 10 year bond earning 3.6% interest. If the total amount of interest from these investments is $5300, determine the amount of principal for each investment.

Answer 1

Hence The amount invested for 5 years is $ 7000 , and The amount invested for 7 years is $ 12000

Explanation:

Given as :

The amount invested in treasury note for 5 years = $ x

the time period = 5 year

The rate of interest applied = 2.8 % at simple interest

So, From simple Interest method :

Simple Interest =
`(\textrm Principal * \textrm Rate* \textrm Time)/(100)`

or,
`SI_1` =
`(\textrm x * \textrm 2.8* \textrm 5)/(100)`

Or,
`SI_1` = 0.14 x

Again ,

The amount invested in treasury note for 10 years = $ x + $ 5000

the time period = 10 year

The rate of interest applied = 3.6 % at simple interest

So, From simple Interest method :

Simple Interest =
`(\textrm Principal * \textrm Rate* \textrm Time)/(100)`

or,
`SI_2` =
`(\textrm( x + 5000) * \textrm 3.6* \textrm 10)/(100)`

Or.
`SI_2` = 0.36 x + 1800

Now , ∵ The total amount of interest from both investment = $ 5300

So,
`SI_1` +
`SI_2` = $ 5300

or, 0.14 x + 0.36 x + $ 1800 = $ 5300

Or, 0.5 x = $ 5300 - $ 1800

or, 0.5 x = 3500

∴ x =
`(3500)/(0.5)`

I.e x = $ 7000

Hence The amount invested for 5 years is $ 7000 , and The amount invested for 7 years is $5000 + $ 7000 = $ 12000 Answer