Question

Complete this activity. Interest at the rates of 5%, 6%, and 8% is earned on investments of $13,000, $12,000, and $4,000 respectively. Calculate the total amount of interest earned as the product of a one-by-three matrix and a three-by-one matrix.

Answer 1

The answer is 1690. First find the amount of interest by a single investment by multiplying the investment amount by the percent interest in decimal form. Then calculate the total by adding up all the products of investment times interest. Matrices will allow to multiply two things together and add the products up all at the same time. So we need to find the investment matrix and interest matrix.

Investment matrix A (transposed)            = (a1 a2 a3) = (13,000 12,000 4,000)

Interest Matrix B                                       = (b1 b2 b3) = (0.05 0.06 0.08)

Amount of interest earned                        = a1b1 + a2b2 + a3b3

Amount of interest earned                        = (0.05) (13,000) + (0.06) (12,000) +                                                                                  (0.08)(4,000)

Amount of interest earned                        = 1690