Question

Vern sold his 1964 ford mustang for $55,000 and wants to invest the money to earn him 5.8% interest per year. he will put some of the money into fund a that earns 3% per year and the rest in fund b that earns 10% per year. how much should he invest into each fund if he wants to earn 5.8% interest per year on the total amount?

Answer 1

To achieve an overall interest rate of 5.8%, Vern should invest $30,000 in Fund A that earns 3% per year and $25,000 in Fund B that earns 10% per year.

Step-by-step explanation:

Vern wants to invest his $55,000 from the sale of his car into two funds, A and B, which earn interest at different rates, to achieve an overall annual interest rate of 5.8%. To find the correct amount to invest in each fund, we can set up a system of equations:

Let x be the amount invested in Fund A and y be the amount invested in Fund B. Thus, x + y = $55,000 because the total investment is $55,000.

The total interest from both investments should be equal to the total investment multiplied by the desired interest rate:

0.03x + 0.10y = 0.058 × 55,000

Now we solve this system of equations. Using the first equation x = 55,000 - y, we can substitute this into the second equation:

0.03(55,000 - y) + 0.10y = 0.058 × 55,000

Simplify and solve for y:

y = $25,000, which is the amount to invest in Fund B at 10%. Using x = 55,000 - y:

x = $30,000, which is the amount to invest in Fund A at 3%.

Therefore, Vern should invest $30,000 in Fund A and $25,000 in Fund B to attain an overall interest rate of 5.8% per year.

Answer 2

The correct answer is, $33000 in Fund A and $22000 in Fund B.

Step-by-step explanation:

Fund A earns 3% per year

Fund B earns 10% per year

Required Rate of return is 5.8%

(Wa x 3%) + [ (1-Wa) ( 10%) ] = 5.8% --- Equation 1

Wa = Weight of funds invested in Fund A

1 - Wa = Weight of funds invested in Fund B

Solving the equation 1 for Wa gives us, Wa = 0.6 and Wb= 0.4

$55000 x 0.6 = $33000

$55000 x 0.4 = $22000