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 %​

Answer 1

Answer:

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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.

Answer: (e)

__________❤____________

Answer 2

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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 +200+ 140

= $ 340.

Total invested amount = 4000 +4000+ 3500

= $7500.

Remaining invest amount = 10000 -10000− 7500

= $ 2500.

We know that, Interest = Principal × Rate × TimeInterest

= $ 160 , Principal = $ 2500,Rate = r Time = 1 year.

160 = 2500 × r × 1.160 = 2500 r 160/2500 = 2500 r /25000.064 = r r = 0.064

Change it to a percent by moving the decimal to the right two places r = 6.4 %

• So correct answer is option (e)