A bank loaned out 64000. Part of the rate at 14% per year and the rest of rate at 4% per year. if the interest received was 5160, how much was loaned at 14%? I'm not too sure how to approach this problem. Thanks in advance for the help.
P= part of the rate at 14 percent.
P*.14+(64000-P).04=5160
solve for P
Understood, so just to clarify the solution is 26000 at 14% correct? thanks for your time.
To solve this problem, we can use a system of equations. Let's set up two equations based on the given information:
Let x be the amount loaned at 14% per year.
Then, the amount loaned at 4% per year would be 64000 - x (since the bank loaned out a total of 64000).
Now, let's calculate the interest earned from each loan:
Interest earned from the loan at 14% per year = x * 0.14
Interest earned from the loan at 4% per year = (64000 - x) * 0.04
According to the problem, the total interest earned is $5160. Therefore, we can set up the equation:
x * 0.14 + (64000 - x) * 0.04 = 5160
Now, let's solve this equation step by step:
0.14x + 0.04(64000 - x) = 5160
0.14x + 2560 - 0.04x = 5160
0.1x + 2560 = 5160
0.1x = 5160 - 2560
0.1x = 2600
x = 2600 / 0.1
x = 26000
Therefore, the amount loaned at 14% per year was $26,000.
In summary, to solve this problem:
1. Set up two equations based on the given information.
2. Calculate the interest earned from each loan.
3. Set up an equation with the total interest earned.
4. Solve the equation to find the amount loaned at 14% per year.