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 %
Answers
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%
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:
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.
Answer: (e)