The controller (money manager) for a small company puts some money in a bank acc

Question

The controller (money manager) for a small company puts some money in a bank account paying 3% per year. He uses some additional money, amounting 1/3 the amount placed in the bank, to buy bonds paying 4% per year. With the balance of the funds, he buys a 10% certificate of deposit. The first year the investments bring a return of $676. If the total of the investments is $10,000 how much is invested at each rate? The controller (money manager) for a small company puts some money in a bank account paying 3% per year. He uses some additional money, amounting 1/3 the amount placed in the bank, to buy bonds paying 4% per year. With the balance of the funds, he buys a 10% certificate of deposit. The first year the investments bring a return of $676. If the total of the investments is $10,000 how much is invested at each rate?

Explanation / Answer

Let,

The amount invested in the bank @ 3% = X

The amount invested in the bond @ 4% = X/3

The amount invested in the COD @ 10% = (10000 – X – X/3)

To value of the investment after 1 year = 10000 + 676 = $10676

Now,

10676 = X*(1+3%) + (X/3)*(1+4%) + (10000 – X – X/3)*(1+10%)

10676 = 1.03X + 1.04X/3 + 10000*1.1 - 1.1X/3)

10676 = 11000 + X*(1.03+ 1.04/3 – (1+1/3)*1.1)

X = (10676 - 11000)/ (1.03+ 1.04/3 – (1+1/3)*1.1)

X = $3600

The amount invested in the bank @ 3% = $3600

The amount invested in the bond @ 4% = $1200

The amount invested in the COD @ 10% = (10000 -3600-1200) = $5200

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