The annual returns on Sid Carrington\'s three investments amounted to $18,560: 6

Question

The annual returns on Sid Carrington's three investments amounted to $18,560: 6% on a savings account, 7% on mutual funds, and 13% on bonds. The amount of Sid's investment in bonds was twice the amount of his investment in the savings account, and the interest earned from his investment in bonds was equal to the dividends he received from his investment in mutual funds. Find how much money he placed in each type of investment. (Let x, y, and z denote the amount, in dollars, in savings, mutual funds, and bonds, respectively.)

The annual returns on Sid Carrington three investments amounted to $18,560: 6% on a savings account, 7% on mutual funds, and 13% on bonds. The amount of Sid's investment in bonds was twice the amount of his investment in the savings account, and the interest earned from his investment in bonds was equal to the dividends he t received from his investment in mutual funds. Find how much money he placed in each type of t. (Let x, y, and z denote the amount, in dollars, in savings, investment mutual funds, and bonds, respectively.) 18,560 0.07y

Explanation / Answer

Let the deposit in Savings is x, in Mutual funds it is y and in Bonds it is z.

we have 6% on savings account , 7% on mutual funds and 13% on bonds.

total annual return is $18560.

so we can say that

0.06x + 0.07y + 0.13z = $18560

The amount of sid's investment in bonds was twice the amount of investment in savings account

so we can say that ,

z = 2z hence 2x - z = 0

and the interest earned from his investment in bonds was equal to the divident from mutual funds hence we can say that,

0.07y = 0.13z

7y - 13z = 0

so we have total 3 equations

0.06x + 0.07y + 0.13z = $18560 --------------1)

2x - z = 0 -----------------2)

7y - 13z = 0 ----------3)

we can write equation 1) as

6x + 7y + 13z = 1856000 -----4)

now put 2x = z and 7y = 13z in equation 4) we have,

3z + 13z + 13z = 1856000

29z = $1856000 so z = $64000

from 2) we have 2x - z = 0 so 2x = z

we have z = $64000

so 2x = $64000 so x = $32000

from 3) we have 7y - 13z = 0 so 7y = 13z

we have z = $64000

so 7y = 13*$64000 so y = $118857.1429

we have,

deposit in Savings is x = $32000

deposit in Mutual funds is y = $118857.1429

deposit in Bonds is z = $64000

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