Michael Perez deposited a total of $4000 with two savings institutions. Bank A pays interest at the rate of 5%/year, whereas Bank B pays interest at the rate of 8%/year. If Michael earned a total of $308 in interest during a single year, how much did he deposit in each institution?
more like Algebra 2, which I'm sure you recall.
If there is $x in bank A, then the rest $(4000-x) is in bank B.
So, now just add up the interest:
.05x + .08(4000-x) = 308
now just crank it out.
Well, well, well, it seems like Michael is quite the savvy investor! Let's solve this financial conundrum, shall we?
Let's assume Michael deposited x dollars in Bank A, which pays 5% interest per year. Based on this, we can determine that he deposited (4000 - x) dollars in Bank B, which offers a more enticing 8% interest rate.
Now, let's calculate the interest earned from each bank. For Bank A, the interest earned can be calculated as follows: 0.05x (since 5% of x is 0.05x). For Bank B, we can find the interest earned by multiplying (4000 - x) by 0.08 (since 8% of (4000 - x) is 0.08(4000 - x)).
Given that the total interest earned is $308, we can set up an equation:
0.05x + 0.08(4000 - x) = 308
Simplifying the equation, we have:
0.05x + 320 - 0.08x = 308
Combining like terms, we get:
-0.03x + 320 = 308
Subtracting 320 from both sides, we have:
-0.03x = -12
Dividing both sides by -0.03, we find:
x ≈ 400
So, Michael deposited approximately $400 in Bank A. As a result, he must've deposited around (4000 - 400) = $3600 in Bank B.
Voila! Michael put $400 in Bank A and $3600 in Bank B. Clown Bot hopes he makes even more money and spreads the joy!
Let's assume Michael deposited x amount in Bank A and (4000 - x) amount in Bank B.
The interest earned in Bank A is calculated as: x * 5% = 0.05x
The interest earned in Bank B is calculated as: (4000 - x) * 8% = 0.08(4000 - x)
According to the given information, the total interest earned is $308. Therefore:
0.05x + 0.08(4000 - x) = 308
0.05x + 320 - 0.08x = 308
-0.03x = -12
x = -12 / -0.03
x = 400
Michael deposited $400 in Bank A and $4000 - $400 = $3600 in Bank B.
To solve this problem, we can set up a system of equations.
Let's assume Michael deposited x dollars in Bank A and y dollars in Bank B.
According to the problem, the total amount deposited is $4000, so we have the equation:
x + y = 4000
We are also given that the interest earned in one year is $308, with Bank A paying an interest rate of 5% and Bank B paying an interest rate of 8%. The interest earned can be calculated using the formula:
Interest = Principal × Rate
For Bank A, the interest earned is 0.05x, and for Bank B, it is 0.08y. So we have another equation:
0.05x + 0.08y = 308
Now we have a system of equations:
x + y = 4000
0.05x + 0.08y = 308
To solve this system, we can use substitution or elimination method.
Let's solve it using the substitution method:
From the first equation, we can express x in terms of y: x = 4000 - y
Substituting x in the second equation, we get:
0.05(4000 - y) + 0.08y = 308
Simplifying, we get:
200 - 0.05y + 0.08y = 308
Combining like terms, we have:
0.03y = 108
Dividing both sides by 0.03, we find:
y = 3600
Substituting this value of y into the equation x + y = 4000, we get:
x + 3600 = 4000
Subtracting 3600 from both sides, we find:
x = 400
So Michael deposited $400 in Bank A and $3600 in Bank B.
Therefore, Michael deposited $400 in Bank A and $3600 in Bank B.