rylie owes $3000 now and $2000 in 4 months. After re - arrangement of payments, he agreed to pay $x in 6 months and $2x in 8 months from now. Determine the value of the $x using now as the focal date and the simple interest rate at 6% per annum.
$x = $2000
$2x = $4000
Using the simple interest formula:
I = Prt
I = 3000 x 0.06 x 6/12
I = $900
3000 + 900 = 3900
3900 - 4000 = -100
Therefore, x = 2000
To determine the value of $x, we can set up an equation based on the given information.
Let's break down the situation:
- Rylie owes $3000 now, which means he has to pay back this amount in 6 months.
- Rylie owes $2000 in 4 months but agreed to delay this payment until 8 months from now, which means he has to pay back this amount in 8 months.
To solve the equation, we'll use the formula for calculating the future value of a present sum with simple interest:
Future value (FV) = Present value (PV) + (PV * interest rate * time)
For the first payment of $3000 in 6 months:
FV1 = PV1 + (PV1 * interest rate * time1)
FV1 = $3000 + ($3000 * 0.06 * 6)
For the second payment of $2000 in 8 months:
FV2 = PV2 + (PV2 * interest rate * time2)
FV2 = $2000 + ($2000 * 0.06 * 8)
Since the total amount Rylie owes should be equal to the sum of these two payments, we can set up the equation:
FV1 + FV2 = $x + $2x
$3000 + ($3000 * 0.06 * 6) + $2000 + ($2000 * 0.06 * 8) = $x + $2x
Now we can solve the equation to find the value of x:
$3000 + ($3000 * 0.36) + $2000 + ($2000 * 0.48) = $x + $2x
$3000 + $1080 + $2000 + $960 = $x + $2x
$7040 = $3x
Dividing both sides by 3:
$7040/3 = $x
Therefore, the value of $x is $2346.67 (rounded to the nearest cent)
To determine the value of x, we need to set up an equation based on the information given and solve for x.
First, let's understand the timeframes and amounts owed:
- Rylie owes $3000 now.
- Rylie will owe $2000 in 4 months.
- After re-arrangement of payments, Rylie will pay $x in 6 months.
- Rylie will pay $2x in 8 months.
Now, let's calculate the interests on the amounts owed:
For the $3000 owed now, we do not need to calculate interest since it is the present value.
For the $2000 owed in 4 months, we need to calculate the interest. The formula for simple interest is: I = PRT, where I is the interest, P is the principal amount, R is the interest rate per period, and T is the number of periods.
In this case, the principal amount is $2000, the interest rate per period is 6% per annum (which means 6% per year divided by 12 months), and the number of periods is 4/12 (since it is 4 months out of a year). Plugging in these values:
I = 2000 * (0.06/12) * (4/12) = $20.
So, in 4 months, Rylie will owe $2000 + $20 = $2020.
Now, let's set up an equation using the present value (3000), future value (2020), interest rate (6%), and time (6 months):
2020 = 3000 * (1 + (0.06/12) * (6/12))
Simplifying the equation:
2020 = 3000 * (1 + (0.06/12) * (1/2))
2020 = 3000 * (1 + 0.005)
2020 = 3000 * 1.005
Dividing both sides by 1.005:
2020 / 1.005 = 3000
2010.95 ≈ 3000
So, after rearranging the payments, Rylie needs to pay approximately $2010.95 in 6 months (or x ≈ 2010.95).
To find the amount Rylie will pay in 8 months (or 2x), we multiply x by 2:
2x = 2 * 2010.95 ≈ $4021.90.
Therefore, Rylie needs to pay approximately $2010.95 in 6 months and $4021.90 in 8 months from now.