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`        A man has \$ 10,000 to invest. He invests \$ 4000 at 5 % and \$ 3500 at 4 %. In order to have a yearly income of \$ 500, he must invest the remainder at:(a) 6 %        , (b) 6.1 %, (c) 6.2 %, (d) 6.3 %, (e) 6.4 %`
3 years ago

```							Income from \$ 4000 at 5 % in one year = \$ 4000 of 5 %.= \$ 4000 × 5/100.= \$ 4000 × 0.05.= \$ 200.Income from \$ 3500 at 4 % in one year = \$ 3500 of 4 %.= \$ 3500 × 4/100.= \$ 3500 × 0.04.= \$ 140.Total income from 4000 at 5 % and 3500 at 4 % = \$ 200 + \$ 140 = \$ 340.Remaining income amount in order to have a yearly income of \$ 500 = \$ 500 - \$ 340.= \$ 160.Total invested amount = \$ 4000 + \$ 3500 = \$7500.Remaining invest amount = \$ 10000 - \$ 7500 = \$ 2500.We know that, Interest = Principal × Rate × TimeInterest = \$ 160,Principal = \$ 2500, Rate = r [we need to find the value of r],Time = 1 year.160 = 2500 × r × 1.160 = 2500r160/2500 = 2500r/2500 [divide both sides by 2500]0.064 = rr = 0.064Change it to a percent by moving the decimal to the right two places r = 6.4 %Therefore, he invested the remaining amount \$ 2500 at 6.4 % in order to get \$ 500 income every year.Answer: (e)
```
3 years ago
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