Answer:
$7,359.65
Step-by-step explanation:
The computation of the amount that to be deposited is shown below:
Here we have to calculate the present value
As we know that
Present value = future value ÷(1+ rate of interest)^years
where,
rate of interest = 12.2% ÷ 4 = 3.05%
And, the years is = 5 × 4 = 20
Now the present value is
= $13,422 ÷ (1+ 3.05%)^20
= $7,359.65
It takes 16 movie rentals for both options to be the same price
<u>Solution:</u>
Given that, A local DVD rental machine rents movies out to customers for $5.75 per movie.
A digital movie company allows you to rent movies for $3.25 but requires a membership fee of $40.
We have to find how many movie rentals will it take for both options to be the same price?
Now, let the number of movies rented be "n"
Then, according to the given information,

Hence, it takes 16 movies to be the same price for both options.
I think that the answer is 120 cubes
We can use the fact that, for
,

Notice that
![\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1{1-x}\right]=\dfrac1{(1-x)^2}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B%5Cdfrac1%7B1-x%7D%5Cright%5D%3D%5Cdfrac1%7B%281-x%29%5E2%7D)
so that
![f(x)=\displaystyle\frac5{(1-x)^2}=5\frac{\mathrm d}{\mathrm dx}\left[\sum_{n=0}^\infty x^n\right]](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdisplaystyle%5Cfrac5%7B%281-x%29%5E2%7D%3D5%5Cfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B%5Csum_%7Bn%3D0%7D%5E%5Cinfty%20x%5En%5Cright%5D)



By the ratio test, this series converges if

so the series has radius of convergence
.