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 with explanation : )

Hey!

Solution:

Income at 5% for $4,000 (1 year)

= 4,000 x 0.05

= $200

Income at 4% for $3,500 (1 year)

= 3,500 x 0.04

= $140

Total Income: 200 + 140 = $340

Remaining Income: 500 - 340 = $160

Total Invested: 4,000 + 3,500 = $7,500

Remaining Invest: 10,000 - 7,500 = $2,500

Formula: Time × Rate × Time = Interest

Principal: $2,500

Interest: $160

r = rate

time = 1 year

1 × r × 2,500 = 160

2,500r = 16

2,500r/2500 = 16/2,500

r = 0.064

0.064 = 6.4%

The final outcome is that the man has $2,500 at 6.4% interest in order to get $500 of income each year. Therefore, the answer is (e) 6.4%.

Hope This Helps :)