Question

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 %​

Answer 1

6.4%

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

160 on 6.4% on 2500

Answer 2

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

Therefore, he invested the remaining amount $ 2500 at 6.4 %. (answer= option e)