Question

A professional athlete deposited an amount of money into a high-yield mutual fund that earns 14% annual simple interest. A second deposit, $2,400 more than the first, was placed in a certificate of deposit earning 8% annual simple interest. In one year, the total interest earned on both investments was $456. How much money was invested in the mutual fund?

Answer 1

Answer:

$1,200

Step-by-step explanation:

Let x be the amount of money deposited in the mutual fund. The interest earned by that investment can be determined as the amount deposited times the interest rate:

$I_{1} = x*0.14$

The value the second deposited can be determined as x+$2,400 and its interest earned is defined in the same manner as the first deposit's:

$I_{2} = (x+2400)*0.08$

The total interest on both investment equals the sum of both interests:

$456=I_{1}+I_{2}\\456=(x+2,400)*0.08 +x*0.14\\x=\frac{456-192}{0.22}\\ x=1,200$

$1,200 were invested in the mutual fund.