Question

Cabin Financial Service Group recommends that a client purchase $10,000 of a corporate bond that earns 7% annual simple interest. How much additional money must be placed in an investment that earns a simple interest rate of 6% so that the total annual interest earned from the two Investments is 6.5% of the total investment?

a) $1,000
b) $500
c) $2,000
d) $1,500

Answer 1

To attain an overall interest rate of 6.5% by investing in bonds with 7% and 6% interest rates respectively, the client needs to invest an additional $10,000 at the 6% rate, making the total investment $20,000.

Step-by-step explanation:

The subject of this question is determining how much additional money needs to be invested at a certain interest rate to achieve a specific overall target interest rate. Now, to solve the original problem, let's define the total amount of money invested as T, and the amount invested at 6% as x. The client has already invested $10,000 at 7%, thus we can set up an equation as follows to represent the total interest earned is 6.5% of T:

0.07($10,000) + 0.06x = 0.065(T)

Since T = $10,000 + x, we have:

$700 + 0.06x = 0.065($10,000 + x)

Solving the equation for x will give us the amount that must be invested at 6% to achieve the overall interest rate of 6.5%. Let's proceed with the algebra:

$700 + 0.06x = $650 + 0.065x

Now, subtract $650 from both sides:

$50 + 0.06x = 0.065x

Then, subtract 0.06x from both sides:

$50 = 0.005x

Finally, divide both sides by 0.005 to find x:

x = $50 / 0.005 = $10,000

So, the client must invest an additional $10,000 at 6% to achieve the desired total interest rate of 6.5% on their total investments.