Question

A $136,000 trust is to be invested in bonds paying 8% CD is paying 7% in mortgages paying 10% the bond and CD investment must equal the mortgage investment to earn a $12,040 annual income from the investments how much should the bank invest in bonds?

Answer 1

The bank should invest $ 48,000 in bonds.

Explanation:

Suppose C, M and B represents the investment in CD, mortgages and bonds respectively,

∵ Total investment = $ 136,000

⇒ B + C + M = 136000 .......(1),

Also, bonds paying 8% CD is paying 7% in mortgages paying 10% the bond,

So, total interest = 8% of B+7% of C+10% of M,

= 0.08B + 0.07C + 0.10M

We have, total interest = $12,040,

0.08B + 0.07C + 0.10M = 12,040

⇒ 8B+7C+10M = 12,04000 .....(2),

Again, the bond and CD investment must equal the mortgage investment,

⇒ B + C = M .......(3),

Equation (1) + equation (3),

2B + 2C = 136000

B + C = 68000 .........(4),

From equation (2) and (3),

8B+7C+10(B+C) = 12,04000

18B + 17C = 12,04000 .....(5)

Equation (5) - 17 × equation (4),

18B - 17 B = 1204000 - 1156000

B = 48000

Hence, the bank should invest $ 48,000 in bonds.