A man has $10,000 to invest. He invests $4,000 at 5% and $3,500 at 4%. In order to have a yearly income of $500, he must invest the remainder at:

1956 AMC 12 Problem 4

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A man has

\$10{,}000

to invest. He invests

\$4{,}000

5\%

and

\$3{,}500

4\%.

In order to have a yearly income of

\$500,

he must invest the remainder at:

6\%

6.1\%

6.2\%

6.3\%

6.4\%

First find both the uninvested principal and the income still needed

The first two investments earn

\$200

and

\$140

per year

The amount left to invest is

10000-4000-3500=2500.

The first two investments earn

0.05(4000)+0.04(3500)=340

dollars, so the remaining investment must earn

500-340=160

dollars. Its required rate is

\frac{160}{2500}=0.064=6.4\%.

Thus, the correct answer is E.