Respuesta :
Using compound interest, it is found that Peter needs to invest $404,054.
What is compound interest?
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:
- 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.
- t is the time in years for which the money is invested or borrowed.
In this problem:
- He plans to make 21 with drawings of $40,000, hence A(t) = 21 x 40,000 = 840,000.
- He will start doing this 15 years from now, hence t = 15.
- The interest is compounded annually, hence n = 1.
- The interest rate is of r = 0.05.
The investment made is P, hence:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]840000 = P\left(1 + \frac{0.05}{1}\right)^{15}[/tex]
[tex]P = \frac{840000}{(1.05)^{15}}[/tex]
[tex]P = 404054[/tex]
Peter needs to invest $404,054.
More can be learned about compound interest at https://brainly.com/question/25781328
