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.
The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
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.
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]15000 = P\left(1 + \frac{0.055}{2}\right)^{2 \times 8}[/tex]
[tex](1.0275)^{16}P = 15000[/tex]
[tex]P = \frac{15000}{(1.0275)^{16}}[/tex]
P = $9,718.11.
She needs to invest $9,781.11 now.
It is given by:
[tex]V(n) = P\left[\frac{(1 + r)^{n-1}}{r}\right][/tex]
In which:
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:
[tex]V(n) = P\left[\frac{(1 + r)^{n-1}}{r}\right][/tex]
[tex]V(n) = 150\left[\frac{(1.005833)^{575}}{0.005833}\right][/tex]
V(n) = $728,753.
You will have $728,753 after 48 years.
More can be learned about compound interest at https://brainly.com/question/25781328
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