Alicia makes two separate investments, one paying 4 percent and the other paying 12 percent simple interest per year.

Question

Alicia makes two separate investments, one paying 44 percent and the other paying 1212 percent simple interest per year. She invests a total of $6600$6600, and her annual interest earnings are $424$424. How much did she invest at each rate?

Answer 1

.12x +(6600-x).04 = 424

.12x-.04x = 424-.04(6600)

.08x = 424-264= 160

x= 160/.08 = 2000 invested at 12%

$4600 invested at 4%

.12(2000) = $240

.04(4600) = $184

240+184= $424

424/6600 = about 6.4% average return

12 is within 5.6 of 6.4

4 is within 2.4 of 6.4

5.6/2.4 = about 2.3

4600/2000= 2.3

she needs about 2.3 times as much

invested at the rate that is closer to 6.4%

2.3 times as much invested at 4%