An investment advisor currently has two types of investments

An investment advisor currently has two types of investments available for clients: a conservative investment A that pays 8% per year and investment B of higher risk that pays 12%. Clients may divide their investments between the two to achieve any total return desired between 8% and 12%. However, the higher the desired return, the higher the risk. If a client wants to invest $42,000 to have desired annual return of $4240, how much money should the client invest in each account to achieve the desired return?

$22,000 for 8% and $20,000 for 12%.

$20,000 for 8% and $22,000 for 12%.

$19,000 for 8% and $23,000 for 12%.

$10,000 for 8% and $32,000 for 12%.

None of the above.

Solution

Let the principle amount with rate of interset be $x. And Total principle amount is $42,000. Therefore principle amount with rate of interest 12% is $(42000-x).

And Interset = P*r*t

Therefore I₁=x*.08*1   and I₂=(42000-x)*.12*1

And total Interest =$4240

4240= .08x + .12(42000-x)

4240=.08x + 5040 -.12x

800= .04x

x=20000

Therefore principle amount with rate of interest 8% is $20000 and with 12% is 42,000-20000=$22,000