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 rema

Question

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 %

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1 month 2021-08-20T06:06:44+00:00 2 Answers 0 views 0

Step-by-step explanation:

Solution:

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 = $2500. We know that, Interest = Principal × Rate × Time Interest =$ 160,

Principal = $2500, Rate = r [we need to find the value of r], Time = 1 year. 160 = 2500 × r × 1. 160 = 2500r 160/2500 = 2500r/2500 [divide both sides by 2500] 0.064 = r r = 0.064 Change it to a percent by moving the decimal to the right two places r = 6.4 % Therefore, he invested the remaining amount$ 2500 at 6.4 % in order to get \$ 500 income every year.