# 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 %

1
by Deleted account

2016-03-31T06:58:32+05:30

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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.