Question

Your aunt receives an inheritance of $20,000. She wants to put some of the money into a savings account that earns 2% interest annually and invest the rest in certificates of deposit (cds) and bonds. A broker tells her that cds pay 5% interest annually and bonds pay 6% interest annually. She wants to earn $1000 interest per year, and she wants to put twice as much money in cds as in bonds. How much should she put in each type of investment?

Answer 1

Answer: She needs to invest $6,000 in bonds, $12,000 in CDs and $2000 in the Savings account to earn a $1000 interest.

We follow these steps in order to arrive at the answer:

Let the amount invested in bonds be x

Since the amount to be invested in CDs is twice the investment in bonds, investment in CDs will 2x.

The amount to be invested in the savings bank will be $20000 - (x+2x)$ or $20,000 - 3x$

The interest earned on bonds will be $0.06x$

The interest earned on CDs will be $2x*0.05 = 0.1x$

The interest earned on the savings banks accounts will be $(20,000-3x)*0.02 = 400-0.06x$

The total expected interest of $1000 is the sum total of the interest earned from each of the three modes of investment.

Hence total interest is:

$1000 = 0.06x + 0.1x+ 400 -0.06x$

Simplifying we get,

$1000 -400 = 0.1x$

$600 = 0.1x$

$\mathbf{x = 6,000}$

Since x represents investments in bonds, the investment in CDs will be $\mathbf{2x = 2*6,000 = 12,000}$

Finally the investments in savings bank will be $\mathbf{20000 - (12,000 + 6,000) = 20,000 - 18,000 = 2,000}$