I really need your help in solving this problem. I really appreciate your time and efforts. Here is the question:
An amount of money invested for 1 year in a savings account will earn $ 1,500. The same amount of money invested in a mini-mall development will earn $6,500 interest in a year, because the interest paid is 10% more than that paid by the savings account. Find the rate of interest paid by each investment?
If the savings account pays x%, then
(x+10)/x = 65/15
x = 3
check:
.03m = 1500
m = 50000
So, $50K was invested
.13(50000) = 6500
Outstanding work Steve, thank you so much!
Yours,
JC
To solve this problem, we need to set up a system of equations. Let's assume the amount of money invested is x, and the interest rate for the savings account is r.
According to the problem, the interest earned by the savings account is $1,500. This can be expressed as:
1) interest from savings account = x * r = $1,500
Now, the interest earned by the mini-mall development is 10% more than that of the savings account. This means the interest rate for the mini-mall development is r + 10% of r, which is 1.1r. The interest earned can be expressed as:
2) interest from mini-mall development = x * 1.1r = $6,500
Now we have a system of two equations (1 and 2) with two variables (x and r). We can solve this system to find the values of x and r.
To solve these equations, divide equation 2 by equation 1:
(x * 1.1r) / (x * r) = $6,500 / $1,500
Simplifying this equation, we get:
1.1r / r = 6,500 / 1,500
The x variables cancel out, and we are left with:
1.1 = 6,500 / 1,500
Now we can solve for r:
1.1 = 4.33
Thus, the interest rate for the savings account, r, is approximately 4.33%.
To find the interest rate for the mini-mall development, we can substitute the value of r back into equation 2:
x * 1.1 * r = $6,500
x * 1.1 * 0.0433 = $6,500
Simplifying this equation, we find:
x = $6,500 / (1.1 * 0.0433)
x ≈ $14,976.95
Therefore, the interest rate for the mini-mall development is approximately 4.33% and the amount of money invested is approximately $14,976.95.
Note: While solving these equations, it's important to be careful with units and make sure expressions are properly simplified along the way.