an executive invests $29,000 some at 7% and some at 6% annual interest. if he receives an annual return of $1870, how much is invested at each rate?
Solve the two simultaneous equiations:
A + B = 29,000
0.06A + 0.07 B = 1870
A is the amount invested at 6%; B is the amount invested at 7%
Find the cost of a home in 20 years, assuming an annual inflation rate of 2%, if the present value of the house is $280,000. (Round your answer to the nearest cent.
To solve this problem, we can use the method of simultaneous equations. Let's call the amount invested at 7% 'x', and the amount invested at 6% 'y'.
We know that the executive invested a total of $29,000, so the first equation is:
x + y = $29,000 -- Equation 1
We also know that the annual return from the investments is $1,870. The interest from the amount invested at 7% is calculated as 0.07x, and the interest from the amount invested at 6% is calculated as 0.06y. So, the second equation is:
0.07x + 0.06y = $1,870 -- Equation 2
Now, we have a system of two equations with two unknowns. We can solve these equations simultaneously to find the values of x and y.
There are different methods to solve these equations, such as substitution or elimination. Let's use the substitution method here:
From Equation 1, we can express x in terms of y as x = $29,000 - y.
We will substitute this value of x into Equation 2:
0.07($29,000 - y) + 0.06y = $1,870
Simplifying this equation gives us:
$2,030 - 0.07y + 0.06y = $1,870
Combining like terms gives:
-0.01y = -$160
To isolate y, we divide both sides of the equation by -0.01:
y = $160 / 0.01
Calculating this expression gives us:
y = $16,000
Now, we can substitute this value of y back into Equation 1 to find the value of x:
x + $16,000 = $29,000
x = $29,000 - $16,000
x = $13,000
Therefore, $13,000 is invested at 7% and $16,000 is invested at 6%.