Question

Davos has $150,000 to invest. His intent is to earn 7.5% interest on his investment. Davos will invest part of the money at 5.6% interest and part at 9.7% interest. How much does Paul need to invest in each option to earn a 7.5% return on the $150,000? Round to the nearest dollar.

Answer 1

The amount invested on 5.6% interest = $80488

The amount invested on 9.7% interest = $69512

Explanation:

Given that total amount of investment = $150,000

Let the amount invested on 5.6% interest = $
`x`

Now, amount invested on 9.7% interest = $(150000-
`x`)

Total interest to be earned = 7.5%

Formula to be used:

`Simple\ Interest = (P* r* t)/(100)`

Where,
`P` is the amount invested

`r` is the rate of interest

`t` is the time for which amount is invested.

As per question statement:

`(x* 5.6)/(100)+((150000-x)* 9.7)/(100)=(150000* 7.5)/(100)\\\Rightarrow 5.6x-9.7x=150000(7.5-9.7)\\\Rightarrow 4.1x=150000* 2.2\\\Rightarrow x = (330000)/(4.1)\\\Rightarrow x \approx \bold{\$80488}`

The amount invested on 5.6% interest = $80488

The amount invested on 9.7% interest = $150000 - $80488 = $69512