How much did he invest at each rate?

Question

Zach invested at a term deposit that paid 4% interest per annum and in a municipal bond that paid 6% interested per annum. If he invested a total of $13,000 and earned $700 interested in a year, how much did he invest at each rate?

 

 

Answer 1

As with all word problems, the first steps are to 1) define variables and then 2) write out equations that express what you're told in the problem.

 

Let x be the amount invested at 4%, and let y be the amount invested at 6%

 

So first of all we know that the total amount invested was 13000.  That means that we can easily get one equation:

 

x + y = 13000

 

Now, how much did he earn on the 4% investment?  That would be 4% of x, or .04x.

 

Similarly, the amount he earned on the 6% investment is .06y.

 

Since the total earnings were $700, that means that .04x + .06y = 700.  That's the second equation.

 

So with two equations in two unknowns (x and y) we should be able to solve.

 

x + y = 13000

.04x + .06y = 700

Let's use substitution.  Find a way to express y in terms of x.  You can do this from the first equation.

x + y = 13000

y = 13000 - x

 

Substitute this expression for y into the second equation.

.04x + .06y = 700

.04x + .06 (13000 - x) = 700

.04x + .06 * 13000 - .06x = 700

.04x + 780 - .06x = 700

-.02x + 780 = 700

-.02x = -80

x = 4000

 

Since y = 13000 - x, that means that y = 9000

 

So he invested 4000 and 4% and 9000 at 6%

 

 

Answer 2

This is a system of equations problem. First, translate what each part of the question is saying.

 

Zach invested at a term deposit that paid 4% interest per annum

⇒ x * 4% = 0.04x

 

and in a municipal bond that paid 6% interested per annum

⇒ y * 6% = 0.06y

 

If he invested a total of $13,000

⇒ x + y = $13,000

 

and earned $700 interested in a year

⇒ (x * 4%) + (y * 6%) = $700

⇒ 0.04x + 0.06y = $700

 

Solve by substitution:

x + y = $13,000 ⇒ x = $13,000 - y

⇒ 0.04($13,000 - y) + 0.06y = $700

⇒ $520 - 0.04y + 0.06y = $700

⇒ 0.02y = $180

⇒ y = $9,000

 

x + y = $13,000

⇒ x + ($9,000) = $13,000

⇒ x = $4,000