If anything is unclear , Please notify me.
I have solved some examples. it's in the picture.
You would do
7(60) + 7(3)
The 60 and 3 came from 63
then to solve it you do
7(60) + 7(3)=
420 + 21=
441
Answer:
hi
Step-by-step explanation:
i think (2x-3)(2x+3)
hope it helps
have a nice day
Answer:
Part a: The Future value of the annuity after 40 years is $518113.24.
Part b: The per year withdrawal in retirement for 25 years will be $48536.19.
Step-by-step explanation:
<em>As the numbers are appearing as a duplication taking all these values as single.</em>
Part a
Future value is given as
![FV=PMT \times [\frac{{(1+I)}^{N}-1}{I}]](https://tex.z-dn.net/?f=FV%3DPMT%20%5Ctimes%20%5B%5Cfrac%7B%7B%281%2BI%29%7D%5E%7BN%7D-1%7D%7BI%7D%5D)
Here
- PMT is the annual value which is $2000 per year
- I is the interest rate which is given as 8%
- N is 40
![FV=PMT \times [\frac{{(1+I)}^{N}-1}{I}]\\\\FV=2000 \times [\frac{({1+.08})^{40}-1}{.08}]\\FV=\$ 518113.03](https://tex.z-dn.net/?f=FV%3DPMT%20%5Ctimes%20%5B%5Cfrac%7B%7B%281%2BI%29%7D%5E%7BN%7D-1%7D%7BI%7D%5D%5C%5C%5C%5CFV%3D2000%20%5Ctimes%20%5B%5Cfrac%7B%28%7B1%2B.08%7D%29%5E%7B40%7D-1%7D%7B.08%7D%5D%5C%5CFV%3D%5C%24%20518113.03)
So the Future value of the annuity after 40 years is $518113.24.
Part b
Per year withdrawal is given as
![PY=\frac{Value}{\frac{1 - \frac{1}{(1+I)^N}}{I}}](https://tex.z-dn.net/?f=PY%3D%5Cfrac%7BValue%7D%7B%5Cfrac%7B1%20-%20%5Cfrac%7B1%7D%7B%281%2BI%29%5EN%7D%7D%7BI%7D%7D)
Here
- PY is the per year withdrawal
- Value is the total amount which is $ 518113 as calculated in part a
- I is the rate of interest which is 8%
- N is 25 years as expected life to live in retirement.
So the value is given as
![PY=\frac{Value}{\frac{1 - \frac{1}{(1+I)^N}}{I}}\\PY=\frac{518113}{\frac{1 - \frac{1}{(1+0.08)^{25}}}{0.08}}\\PY=\frac{518113}{10.6747}\\PY=\$ 48536.19](https://tex.z-dn.net/?f=PY%3D%5Cfrac%7BValue%7D%7B%5Cfrac%7B1%20-%20%5Cfrac%7B1%7D%7B%281%2BI%29%5EN%7D%7D%7BI%7D%7D%5C%5CPY%3D%5Cfrac%7B518113%7D%7B%5Cfrac%7B1%20-%20%5Cfrac%7B1%7D%7B%281%2B0.08%29%5E%7B25%7D%7D%7D%7B0.08%7D%7D%5C%5CPY%3D%5Cfrac%7B518113%7D%7B10.6747%7D%5C%5CPY%3D%5C%24%2048536.19)
So the per year withdrawal in retirement for 25 years will be $48536.