Question

One safe investment pays 10% per year, and a more risky investment pays 18% per year. A woman who has $142,900 to invest would like to have an income of $19,490 per year from her investments. How much should she invest at each rate?

10%	$
18%	$

Answer 1

Return Required = 19490 / 142900

= 13.64%

Let the weight of investment in safe investment be X

then the weight of investment in risky investment be 1-X

Return Required = Weighted Return

13.64% = X * 10% + (1-X) * 18%

13.64% = 10%*X + 18% - 18%*X

13.64% = 18% - 8%*X

X = (18% - 13.64%) / 8%

X = 0.545 oR 54.5%

Proportion invested in Safe investment = 0.545

Proportion invested in Risky investment = 1 - 0.545 = 0.455

Amount invested in Safe investment = 0.545 * 142900 = 77880.5

Amount invested in Risky investment = 0.455 * 142900 = 65019.5