Question

Maricopa's Success scholarship fund receives a gift of $ 145000. The money is invested in stocks, bonds, and CDs. Stocks pay 6. 7 % interest, bonds pay 2. 5 % interest, and CDs pay 5. 75 % interest. Maricopa Success invests $ 10000 more in bonds than in CDs. If the annual income from the investments is $ 6977. 5 , how much was invested in each account?

Maricopa Success invested $ in stocks. Maricopa Success invested $ in bonds. Maricopa Success invested $ in CDs

Answer 1

Let x be the amount invested in CDs.

Then, the amount invested in bonds is x + $10,000.

The amount invested in stocks is $145,000 - (x + x + $10,000) = $125,000 - 2x - $10,000 = $115,000 - 2x.

The annual income from the stocks is 6.7% of ($115,000 - 2x), which is 0.067($115,000 - 2x) = $7715 - 0.134x.

The annual income from the bonds is 2.5% of (x + $10,000), which is 0.025(x + $10,000) = $250 + 0.025x.

The annual income from the CDs is 5.75% of x, which is 0.0575x.

The total annual income is $7715 - 0.134x + $250 + 0.025x + 0.0575x = $6977.5.

Simplifying and solving for x, we get:

0.9485x + $7465 = $6977.5

0.9485x = $-487.5

x = $513.56 (rounded to the nearest penny)

Therefore, Maricopa Success invested $115,000 - 2x = $113,972.88 in stocks, $10,000 + x = $10,513.56 in bonds, and x = $513.56 in CDs.