For each situation, we have that:
11) Using compound interest, it is found that she needs to invest $9,781.11 now.
12) Using the future value formula, it is found that you will have $728,753 after 48 years.
<h3>What is compound interest?</h3>
The amount of money earned, in compound interest, after t years, is given by:
In which:
- A(t) is the amount of money after t years.
- P is the principal(the initial sum of money).
- r is the interest rate(as a decimal value).
- n is the number of times that interest is compounded per year.
For this problem, the parameters are given as follows:
A(t) = 15000, t = 4, r = 0.055, n = 2.
Hence we solve for P to find the amount that needs to be invested.
P = $9,718.11.
She needs to invest $9,781.11 now.
<h3>What is the future value formula?</h3>
It is given by:
![V(n) = P\left[\frac{(1 + r)^{n-1}}{r}\right]](https://tex.z-dn.net/?f=V%28n%29%20%3D%20P%5Cleft%5B%5Cfrac%7B%281%20%2B%20r%29%5E%7Bn-1%7D%7D%7Br%7D%5Cright%5D)
In which:
- n is the number of payments.
For item 12, the parameters are given as follows:
P = 150, r = 0.07/12 = 0.005833, n = 48 x 12 = 576.
Hence the amount will be given by:
![V(n) = 150\left[\frac{(1.005833)^{575}}{0.005833}\right]](https://tex.z-dn.net/?f=V%28n%29%20%3D%20150%5Cleft%5B%5Cfrac%7B%281.005833%29%5E%7B575%7D%7D%7B0.005833%7D%5Cright%5D)
V(n) = $728,753.
You will have $728,753 after 48 years.
More can be learned about compound interest at brainly.com/question/25781328
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