If the annual income from the investments is $ 5110 , how much was invested in each account?

Question

Maricopa's Success scholarship fund receives a gift of $ 125000. The money is invested in stocks, bonds, and CDs. CDs pay 5 % interest, bonds pay 2.4 % interest, and stocks pay 11 % interest. Maricopa Success invests $ 75000 more in bonds than in CDs. If the annual income from the investments is $ 5110 , how much was invested in each account?

Answer 1

Assuming simple interest rather than compound, let C represent the amount invested in CDs and S in stocks. Then:

C + (75000+C) + S = 125000 -> 2C + S = 50000

0.05C + 0.024(75000+C) + 0.11S = 5110 = 0.074C + 1800 + 0.11S -> 3310 - 0.074C = 0.11S ->

S = (3310 - 0.074C)/0.11

2C + (3310 - 0.074C)/0.11 = 50000 -> 0.22C + 3310 - 0.074C = 5500 -> 0.146C = 2190 -> C = 15,000

So 15,000 was invested in CDs, 90,000 in bonds and 20,000 in stocks

Answer 2

x=stocks, y = bonds, z = CDs

x+ y + z = 125000

y = z + 75000

0.11x + 0.024y + 0.05z = 5110

x + z + 75000 + z = 125000

x + 2z = 50000

x = 50000 - 2z

0.11x + 0.024(z + 75000) + 0.05z = 5110

0.11x + 0.024z + 1800 + 0.05z = 5110

0.11x + 0.074z + 1800 = 5110

0.11x + 0.074z = 3310

0.11(5000 - 2z) + 0.074z = 3310

5500 - 0.22z + 0.074z = 3310

5500 - 0.146z = 3310

-0.146z = -2190

z = 1500

x = 50000 - 2(15000)

= 50000 - 30000

= 20000

x+y+z = 125000

20000+y+ 15000 = 125000

35000 + y = 125000

y = 90000

yes , it checks out