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Fittoniya [83]
1 year ago
5

Ms. Whodunit needs $15 000 to go on her dream vacation in four years. How much

Mathematics
1 answer:
lisov135 [29]1 year ago
6 0

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:

A(t) = P\left(1 + \frac{r}{n}\right)^{nt}

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.

A(t) = P\left(1 + \frac{r}{n}\right)^{nt}

15000 = P\left(1 + \frac{0.055}{2}\right)^{2 \times 8}

(1.0275)^{16}P = 15000

P = \frac{15000}{(1.0275)^{16}}

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]

In which:

  • P is the payment.
  • n is the number of payments.
  • r is the interest rate.

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) = P\left[\frac{(1 + r)^{n-1}}{r}\right]

V(n) = 150\left[\frac{(1.005833)^{575}}{0.005833}\right]

V(n) = $728,753.

You will have $728,753 after 48 years.

More can be learned about compound interest at brainly.com/question/25781328

#SPJ1

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