Q: Ms. Parker deposits $8000 in one simple interest account and $2000 in a second simple interest account. The interest rate on the $8000 account is 2% more than the rate on the $2000 account. If the total yearly amount of interest earned on the $8000 account is $459 more than the interest earned on the $2000 account. Find the interest rate on each account. Please answer in complete details?
rate of first account --- r , the rate in decimals
rate on 2nd account --- r+.02
interest on 1st account = 2000r
interest on 2nd account = 8000(r + .02)
8000(r + .02) - 2000r = 459
8000r + 160 - 2000r = 459
6000r = 299
r = 299/6000 = .0498333
= appr 4.98%
the lower rate is 4.98% , the higher rate is 6.98%
check:
4.98% of 2000 = 99.67
6.98% of 8000 = 558.67
the differ by $459
Yeah!!
A: Well, that's quite the math question! Let's break it down, shall we?
Let's start by assuming the interest rate on the $2000 account is 'x' percent. That means the interest rate on the $8000 account would be 'x + 2' percent, since it's 2% more.
Now, let's calculate the interest earned on each account. The interest earned on the $8000 account would be (8000 * (x + 2))/100, and the interest earned on the $2000 account would be (2000 * x)/100.
The problem tells us that the total yearly interest earned on the $8000 account is $459 more than the interest earned on the $2000 account. So we can write an equation:
(8000 * (x + 2))/100 = (2000 * x)/100 + 459
To make things easier, let's get rid of those pesky fractions by multiplying both sides of the equation by 100:
8000 * (x + 2) = 2000 * x + 45900
Now, let's simplify it:
8000x + 16000 = 2000x + 45900
Subtract 2000x from both sides:
6000x + 16000 = 45900
Subtract 16000 from both sides:
6000x = 29900
Divide both sides by 6000:
x = 29900/6000
x ≈ 4.9833
So, the interest rate on the $2000 account is approximately 4.9833%. Since the interest rate on the $8000 account is 2% more, the interest rate on that account would be approximately 6.9833%.
Keep in mind that due to rounding, these numbers may not be exact, but they should be pretty close!
I hope this helps, and remember, math can be funny too!
Let's denote the interest rate on the $2000 account as "x%".
According to the given information, the interest rate on the $8000 account is 2% more than the rate on the $2000 account.
So, the interest rate on the $8000 account can be expressed as "x + 2%".
Now, let's calculate the interest earned on each account.
For the $8000 account, the amount of interest earned can be calculated using the formula:
Interest = Principal * Rate * Time
Since the principal (amount deposited) is $8000, the rate is (x + 2)% or (x + 2)/100, and the time is 1 year, we can write the equation for the interest earned on the $8000 account as:
Interest_8000 = 8000 * (x + 2)/100 * 1
For the $2000 account, the amount of interest earned can be calculated using the same formula:
Interest_2000 = 2000 * x/100 * 1
According to the given information, the total yearly amount of interest earned on the $8000 account is $459 more than the interest earned on the $2000 account.
So, we can write the equation:
Interest_8000 = Interest_2000 + 459
Now, substitute the values of Interest_8000 and Interest_2000 in terms of x:
8000 * (x + 2)/100 * 1 = 2000 * x/100 * 1 + 459
Simplifying the equation:
80(x + 2) = 20x + 459
80x + 160 = 20x + 459
60x = 299
x = 299/60
x ≈ 4.983
Therefore, the interest rate on the $2000 account is approximately 4.983%.
Now, substitute this value of x back into the equation for the interest rate on the $8000 account:
Interest rate on the $8000 account = x + 2%
≈ 4.983 + 2%
≈ 6.983%
Therefore, the interest rate on the $8000 account is approximately 6.983%.
To solve this problem, we can start by setting up an equation based on the given information.
Let's assume the interest rate on the $2000 account is "x%". According to the given information, the interest rate on the $8000 account is 2% more than the rate on the $2000 account. Therefore, the interest rate on the $8000 account is (x + 2)%.
Now, let's calculate the interest earned on each account. The formula for calculating simple interest is:
Interest = Principal * Rate * Time
For the $2000 account, the interest earned can be calculated as:
Interest1 = 2000 * (x/100) * 1 (1 year)
For the $8000 account, the interest earned can be calculated as:
Interest2 = 8000 * ((x + 2)/100) * 1 (1 year)
According to the problem, the total yearly amount of interest earned on the $8000 account is $459 more than the interest earned on the $2000 account. So, we can write the following equation:
Interest2 - Interest1 = 459
Substituting the values of Interest1 and Interest2, we get:
8000 * ((x + 2)/100) * 1 - 2000 * (x/100) * 1 = 459
Simplifying the equation, we have:
8000 * (x + 2)/100 - 2000 * x/100 = 459
80(x + 2) - 20x = 459 (dividing both sides by 100)
80x + 160 - 20x = 459
60x + 160 = 459
Subtracting 160 from both sides, we get:
60x = 299
Dividing both sides by 60, we get:
x = 299/60 ≈ 4.983
Therefore, the interest rate on the $2000 account is approximately 4.983%, and the interest rate on the $8000 account is approximately (4.983 + 2)% = 6.983%.
So, the interest rate on the $2000 account is approximately 4.983%, and the interest rate on the $8000 account is approximately 6.983%.