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

Answer:

The amount invested on 5.6% interest = $80488

The amount invested on 9.7% interest = $69512

Step-by-step 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:

$Simple\ Interest = \dfrac{P\times r\times t}{100}$

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:

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

The amount invested on 5.6% interest = $80488

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