Question

One safe investment pays 7​% per​ year, and a more risky investment pays 13​% per year.

a. How much must be invested in each account if an investor of $99,000 would like a return of $8,430 per​ year?

b. Why might the investor use two accounts rather than put all the money in the 13​% investment?

Answer 1

Safe investment pays =7%

Risky investment pays = 13%

a) Return of $8,430

Amount to Invest = 99,000

Let say amount invested in risky investment be X, thus amount invested in safe investment is 99,000 - X.

X * 0.13 + 0.07 (99,000 - X) = 8,430

0.13X + 6,930 - 0.07X = 8,430

X = 25,000

Thus amount invested in safer investment is 99,000 - 25,000 = 74,000 while mount invested in risky investment is 25,000

b) Investor use two accounts because she wants to diversify their investment such that if risky investment turn out to be more lemon, she will loose more of the money. So she invest in safe investment such that she can cover some of the money if she loose some in risky investment.