As part of his retirement strategy, John plans to invest $210,000 in two different funds. He projects that the moderately high risk investments should return, over time, about 9% per year, while the low risk investments should return about 4% per year. If he wants a supplemental income of $11,400 a year, how should he divide his investments?

Given John plans to invest $210,000 in two different funds. He projects that the moderately high risk investments should return, overtime 9% per year,while low risk investments should return about 4% per year.

He wants a supplemental income of$11,400 a year.

Let , he invested $x at 9% per year and $(210,000-x) at 4% per year.

[tex]interest=\frac{prt}{100}[/tex] p = principle , r = rate of interest and t = time

The interest earns at 9% per year= [tex]\frac{x\times 9\times 1}{100}[/tex]

The interest earns at 4% per year=[tex]\frac{(210,00-x)\times 4 \times 1}{100}[/tex]

According to the problem,

[tex]\frac{x\times 9\times 1}{100}+\frac{(210,00-x)\times 4 \times 1}{100}= 11400[/tex]

[tex]\Leftrightarrow 9x+840000-4x=11400 \times 100[/tex]

[tex]\Leftrightarrow 5x=1140000-840000[/tex]

[tex]\Leftrightarrow x=\frac{300000}{5}[/tex]

[tex]\Leftrightarrow x=60,000[/tex]

Therefore he invested $60,000 at 9% per year and $(210,000-60,000)=$150,000 at 4% per year.