how much was invested in each vehicle

Question

Country Day's scholarship fund receives a gift of $ 140000. The money is invested in stocks, bonds, and CDs. CDs pay 4.75 % interest, bonds pay 4.2 % interest, and stocks pay 11.7 % interest. Country day invests $ 45000 more in bonds than in CDs. If the annual income from the investments is $ 8670 , how much was invested in each vehicle? 

Answer 1

Hi Najma, you need to set up an equation that represents all of the money involved. Let x represent the money invested in CDs. Since $45000 more was invested in bonds than in CDs, x + 45000 represents the money invested in bonds. The difference in the money invested in CDs plus the money invested in bonds represents the money invested in stocks.

Money invested in CDs = x

Money invested in bonds = x + 45000

Money invested in stocks = 140000 - (x + (x + 45000) = 95000 - 2x

Equation to solve:

.0475x + .042 * (x + 45000) + .117 * (95000 - 2x) = 8670

Solve this equation for x.

Questions?

Answer 2

let investment in CDs = x Investment in Bonds = x + 45000 Investment in Stock = 140000- (x + x + 45000) = 95000 -2x

8670 = CDs + Bonds + Stocks

8670 = x × 4·75% + ( x + 45000 ) × 4·2% + ( 95000 - 2x) × 11·7

8670 = 4·75 + 4·2x + 189000 + 1111500 - 23·4x / 100

867000 = 1300500 - 14·45x

x = 1300500 - 867000 / 14·45 = 30000

∴ CDs = x = $ 30000

bonds= x + 45000 = 30000 + 45000 = $ 75000/-

Stock = 95000 - 2x = 95000 - 2×30000 = $ 35000/-

check = 30000 + 75000 + 35000 = 140000

Answer 3

Suppose c in CDs

Then 45000 + c in bonds

140000 - c - (45000 + c) = 95000 -2c in stocks

Interest

stocks 11.7% of (95000 - 2c) = 0.117 (95000 - 2c)

bonds 4.2% of (45000 + c) = 0.042 (45000 + c)

CDs 4.75 % of c = 0.0475 c

add up the three interests, set total equal to 8670, solve for c, then find bonds and stocks