Current amount in account
P=36948.61
Future value of this amount after n years at i=11% annual interest
F1=P(1+i)^n
=36948.61(1.11)^n
Future value of $3000 annual deposits after n years at i=11%
F2=A((1+i)^n-1)/i
=3000(1.11^n-1)/0.11
We'd like to have F1+F2=280000, so forming following equation:
F1+F2=280000
=>
36948.61(1.11)^n+3000(1.11^n-1)/0.11=280000
We can solve this by trial and error.
The rule of 72 tells us that money at 11% deposited will double in 72/11=6.5 years, approximately.
The initial amount of 36948.61 will become 4 times as much in 13 years, equal to approximately 147800 by then.
Meanwhile the 3000 a year for 13 years has a total of 39000. It will only grow about half as fast, namely doubling in about 13 years, or worth 78000.
Future value at 13 years = 147800+78000=225800.
That will take approximately 2 more years, or 225800*1.11^2=278000.
So our first guess is 15 years, and calculate the target amount
=36948.61(1.11)^15+3000(1.11^15-1)/0.11
=280000.01, right on.
So it takes 15.00 years to reach the goal of 280000 years.
(-4) - (- 8) + (- 4)
- 4 - (- 8) + (- 4)
- 4 + 8 + (- 4 )
- 4 + 8 - 4
= 0
Answer:
x=3. y=6
Step-by-step explanation:
So, to solve x and y, we need to take the equivelent sides of the two triangles, take their equations, and solve them.
So to find what x equals, we can take the 13, and make it equal to the 4x+1:
13=4x+1
Subtract the one from both sides:
12=4x
Divide both sides by 4:
3=x
Or
<u>x=3</u>
So we know the x value is 3.
Now lets solve for y using the bottom equations:
2x+y=8x-2y
Subtract 1y from both sides:
2x=8x-3y
Subtract 8x from both sides:
-6x=-3y
Divide both sides by -6:
x=1/2y
So we already know that x=3, lets plug that in for x, and solve for y:
3=1/2y
Or
1/2y=3
Multiply both sides by 2 to get 1y:
<u>y=6</u>
So we know that y is equal to 6.
Hope this helps!
Answer:
4/5 and 5/2
Step-by-step explanation:
took it
