12/3 = x/8
Cross multiply
3x = 96
Eliminate
3x/3 = 96/3
x = 32
Answer:
you do you like to school
so I can see what
Answer:
GPA stands for grade point average. the highest you can get is 4.5. There is no such things as a 95 GPA. To calculate, take the number or point per grade you have, A is 4.0, B is 3.0, C is 2.0, and so on, and add them all up and then divide by the number of classes you are taking.
Step-by-step explanation:
In order to find the original price, we need to divide by 4. This is because the price was reduced by 20%, it is 4/5 of the original price.
By dividing by 4, we can see that 90.40 is 22.60.
To find the original price, we add 22.60 (1/5 of the original price), to 90.40 (4/5 the original price) to find that $113 is the original price.
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.
