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:

Step-by-step explanation:

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

Given :-- he invest 4000 at 5% , 3500 at 4% and overall profit is 500 .

Solution :---

We know that, interest he got from sum at R% is our income ..

so,

SI = P*R*T/100

interest he earn from 4000 =

SI = 4000*5*1/100 = 200 rs.

interest he earn from 3500 =

SI = 3500*4*1/100 = 140

Total interest he got now = 200+140 = 340 .

in order to earn 500 he must have = 500-340 = 160rs from rest amount ..

Rest amount = 10000-4000-3500 = 2500

so,

Rate = SI*100/P*T

Rate % = 160*100/2500*1 = 6.4% (E) (Ans)