A bank loaned out $53,000, part of it at a rate of 12% per year and the rest at a rate of 5% per year. If the interest received was $4960, how much was loaned at 12%?
Show all work.
This just like the mixture problems with nuts, acid, etc.
x = amt at 12%
y = amt at 5%
total interest:
x + y = 53000
.12x + .05y = 4960
.12x + .12y = 6360
.12x + .05y = 4960
.07y = 1400
y = 20000 at 5%
x = 33000 at 12%
Ah, the bank's financial drama! Let's dive into the numbers.
Let's assume that the amount loaned at a rate of 12% is x dollars. So, the amount loaned at a rate of 5% would be (53000 - x) dollars.
Now let's calculate the interest earned from each loan amount:
For the loan at 12%, the interest earned would be (x * 12%).
For the loan at 5%, the interest earned would be ((53000 - x) * 5%).
Since the total interest received is $4960, we can create the following equation:
(x * 12%) + ((53000 - x) * 5%) = $4960
Now let's solve it step by step, and hopefully, laughter will follow!
First, let's solve for the interest earned from the loan at 12%. Multiplying x by 12% gives us 0.12x.
Next, we'll solve for the interest earned from the loan at 5%. Multiplying (53000 - x) by 5% gives us 0.05(53000 - x).
Now we can express the equation in terms of x:
0.12x + 0.05(53000 - x) = $4960
Let's multiply 0.05 by both terms inside the parentheses:
0.12x + 0.05 * 53000 - 0.05x = $4960
Doing some quick math:
0.12x + 2650 - 0.05x = $4960
Combining like terms:
0.07x + 2650 = $4960
Now let's subtract 2650 from both sides:
0.07x = $2310
Finally, we'll divide both sides by 0.07 to find x:
x = $2310 / 0.07
And with a final bit of silliness, we find:
x ≈ $33,000
So, approximately $33,000 was loaned at a rate of 12%. The rest, $20,000, was loaned at a rate of 5%. Hurray for finances!
Let's assume that the amount loaned at 12% is x dollars.
Therefore, the amount loaned at 5% would be ($53,000 - x) dollars.
The interest earned from the amount loaned at 12% would be x * 12% = 0.12x dollars.
The interest earned from the amount loaned at 5% would be ($53,000 - x) * 5% = 0.05($53,000 - x) dollars.
Since the total interest earned is $4960, we can set up the equation as follows:
0.12x + 0.05($53,000 - x) = $4960
Now let's solve the equation step by step:
0.12x + 0.05($53,000 - x) = $4960
0.12x + 0.05($53,000) - 0.05x = $4960
0.12x + $2650 - 0.05x = $4960
0.07x + $2650 = $4960
0.07x = $4960 - $2650
0.07x = $2310
Now let's solve for x:
x = $2310 / 0.07
x ≈ $33,000
Therefore, approximately $33,000 was loaned at a rate of 12%.
To solve this problem, let's represent the amount loaned at 12% as 'x' and the amount loaned at 5% as 'y'.
We know that the bank loaned out $53,000, so we have the equation:
x + y = $53,000
We also know that the interest received was $4,960. The interest on the amount loaned at 12% can be calculated by multiplying the amount (x) by the rate (12%) and dividing by 100:
(x * 12) / 100
Likewise, the interest on the amount loaned at 5% can be calculated by multiplying the amount (y) by the rate (5%) and dividing by 100:
(y * 5) / 100
Since the total interest received is $4,960, we can set up another equation:
(x * 12) / 100 + (y * 5) / 100 = $4,960
Now we have a system of two equations:
x + y = $53,000
(x * 12) / 100 + (y * 5) / 100 = $4,960
To solve the system, we'll use the substitution method.
1. Solve the first equation for x:
x = $53,000 - y
2. Substitute the value of x in the second equation:
(($53,000 - y) * 12) / 100 + (y * 5) / 100 = $4,960
3. Simplify and solve for y:
(12($53,000) - 12y + 5y) / 100 = $4,960
(12($53,000) - 7y) / 100 = $4,960
(12($53,000) = 7y + $4,96000
$636,000 = 7y + $4,96000
$636,000 - $4,96000 = 7y
$86000 = 7y
$86000/7 = y
y = $12,286
4. Substitute the value of y back into the first equation to solve for x:
x = $53,000 - y
x = $53,000 - $12,286
x = $40,714
Therefore, $40,714 was loaned at 12%.