Question
Asked Nov 7, 2019

one safe investment pays 10% per year, and a riskier investment pays 18% per year. A woman who has $145,600 to invest would like to have an income of $20,000 per year from her investments. How much should she invest at each rate?

check_circleExpert Solution
Step 1

Let x be the amount invested on safer investment pays 10% per year and y be the amount invested on risker investment pays 18% per year.

Given,

A woman has $145,600 to invest
i.e.
xy145600
..1)
x 145600- y
and the woman likes to have an income of $20,000 per year from her investments
i.e.
10%x+18%y 20000
..(2)
0.1x 0.18y 20000
help_outline

Image Transcriptionclose

A woman has $145,600 to invest i.e. xy145600 ..1) x 145600- y and the woman likes to have an income of $20,000 per year from her investments i.e. 10%x+18%y 20000 ..(2) 0.1x 0.18y 20000

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Step 2

Substitute x=145600-y in equati...

0.1(145600-y)+0.18y = 20000
0.08y 20000-14560
0.08 y 5440
y68000
Substitute y value in (1), we get
x145600-68000
x 77600
help_outline

Image Transcriptionclose

0.1(145600-y)+0.18y = 20000 0.08y 20000-14560 0.08 y 5440 y68000 Substitute y value in (1), we get x145600-68000 x 77600

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