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sertanlavr [38]
2 years ago
10

5. 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 %​
Business
2 answers:
Len [333]2 years ago
4 0
6.4%

200 from the 5% of 4000
140 from 4% on 3500

160 on 6.4% on 2500
snow_lady [41]2 years ago
4 0
<h3><em><u>solution</u></em><em><u>:</u></em></h3>

<em><u>Income from $ 4000 at 5 % in one year = $ 4000 of 5 %.</u></em>

<em><u>= $ 4000 × 5/100</u></em>

<em><u>= $ 4000 × 0.05</u></em>

<em><u>= $ 200</u></em>

<em><u>Income from $ 3500 at 4 % in one year = $ 3500 of 4 %.</u></em>

<em><u>=</u></em><em><u> </u></em><em><u>$ 3500 × 4/100</u></em>

<em><u>= $ 3500 × 0.04</u></em>

<em><u>= $ 140</u></em>

<em><u>Total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $ 140 = $ 340.</u></em>

<em><u>Remaining income amount in order to have a yearly income of $ 500 = $ 500 - $ 340.</u></em>

<em><u>=</u></em><em><u> </u></em><em><u>$ 160</u></em>

<em><u>Total invested amount </u></em>

<em><u>= $ 4000 + $ 3500 </u></em>

<em><u>= $7500</u></em>

<em><u>Remaining invest amount </u></em>

<em><u>= $ 10000 - $ 7500 </u></em>

<em><u>= $ 2500</u></em>

<em><u>We know that, Interest = Principal × Rate × Time</u></em>

<em><u>Interest = $ 160</u></em>

<em><u>Principal = $ 2500</u></em>

<em><u>Rate = r [we need to find the value of r]</u></em>

<em><u>Time = 1 year</u></em>

<em><u>160 = 2500 × r × 1</u></em>

<em><u>160 = 2500r</u></em>

<em><u>160/2500 = 2500r/2500 [divide both sides by 2500</u></em>

<em><u>0.064 = r</u></em>

<em><u>r = 0.064</u></em>

<em><u>Therefore, he invested the remaining amount $ 2500 at 6.4 %</u></em><em><u>.</u></em><em><u> </u></em><em><u>(</u></em><em><u>answer</u></em><em><u>=</u></em><em><u> </u></em><em><u>option</u></em><em><u> </u></em><em><u>e</u></em><em><u>)</u></em>

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