Question

A $1200 investment is made. How much should be invested at 15% and how much at 8% so that the total return on the entire investment is 9.5%?

Answer 1

The amount invested at 15% = $257.14

The amount invested at 8% = $942.86

Explanation:

Let the amount invested at:

15% = a

8% = b

Total invesment = $1200

Hence:

a + b= $1200....... Equation 1

a = 1200 - b

15% × a + 8% × b = 9.5% × 1200

0.15a + 0.08b = 0.095 × 1200

0.15a + 0.08b = 114..... Equation 2

We substitute 1200 - b for a in Equation 2

0.15(1200 - b) + 0.08b = 114

180 - 0.15b + 0.08b = 114

- 0.15b + 0.08b = 114 - 180

- 0.07b = - 66

b = -66/-0.07

b = $942.85714286

Approximately = $942.86

Note that:a = 1200 - b

a = $1200 - $942.86

a = $257.14