Question

Allison ivested $40,000 that she areceived in an inheritance. Part of the money was invested in a certificate of deposit that paid 3.2% for the year while the remainder of the money was invested in a mutual fund that returned 8.4% for the year. The combined income from the investments for the year was $2736. How much did Allison invest at each rate? (For full credit, set up and solve a linear system using either elimination or subtitution. Clearly label any variables you introduce. Write your answer as a sentence)

Answer 1

Let the amount invested by Allison in the certificate of deposit that paid 3.2% for the year be $ x. Then the amount invested by Allison in the mutual fund that returned 8.4% for the year is $ (40000-x).

The interest on the certificate of deposit for an year is x*3.2 % = 3.2x/100 = 4x/125 and the interest on the mutual fund for an year is (40000-x)*8.4 % = (84/1000)(40000-x) = 3360-21x/250. Further, since the combined income from the two investments for the year was $2736, hence 4x/125 + 3360 -21x/250 = 2736 or, 21x/250-4x/125 = 3360-2736 or, 13x/250 = 624 so that x = 624*250/13 = 12000. Then 40000-x = 28000.

Thus, the amounts invested by Allison in the certificate of deposit at 3.2 % and the mutual fund at 8.4 % were $ 12000 and $ 28000 respectively.