Question

Country Day's scholarship fund receives a gift of $ 155000. The money is invested in stocks, bonds, and CDs. CDs pay 5.5 % interest, bonds pay 5.9 % interest, and stocks pay 10.7 % interest. Country day invests $ 60000 more in bonds than in CDs. If the annual income from the investments is $ 12705, how much was invested in each vehicle? in stocks. Country Day invested $ Country Day invested $ Country Day invested $ in bonds. in CDs.

Answer 1

Total fund received is $155000

Interest rate of CDs is 5.5%

Interest rate of bonds is 5.9%

Interest rate of stocks pay 10.7%

Let money invested in CDs be x

Let the money invested in stocks be y

Country day invests $60000 more in bonds than in CDs

Money invested in bonds is $60000 +x

Total investment is $155000

x+y+60000+x=155000

2x+y=95000

y=95000-2x ............equation 1

Annual income from CDs is

$Simple \; Interest=\frac{p \times r \times t}{100}$

  $=\frac{x \times 5.5 \times 1}{100}$$=\frac{x \times 5.5 \times 1}{100}= 0.055x$

Annual income from stocks is

$=\frac{y \times 10.7 \times 1}{100}= 0.107(95000-2x)$

y=95000-2x from equation 1

Annual income from bonds is

$=\frac{(60000+x) \times 5.9 \times 1}{100}=\frac{354000+ 5.9 x}{100} =3540+0.059x$

Total income from all the sources is

0.055x+0.107(95000-2x)+3540+0.059x=12705

$x=\$10000$

Money invested in CDs is $10,000

y=95000-2x from equation 1

y=95,000-2(10,000)

y=$75,000

Money invested in stocks is $75,000

Money invested in bonds is $60000 +x

60,000+10,000=$70,000

Money invested in bonds is $70,000

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