Respuesta :
Using compound interest, it is found that he must deposit $56,389.
Compound interest:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
- 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:
- Hopes to have $80,000 in 20 years, thus [tex]t = 20, A(t) = 80000[/tex].
- Interest rate of 1.75%, thus [tex]r = 0.0175[/tex].
- Compounding monthly, thus [tex]n = 12[/tex]
- The investment is of P, for which we have to solve.
Then:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]80000 = P(1 + \frac{0.0175}{12})^{12(20)}[/tex]
[tex]P = \frac{80000}{(1 + \frac{0.0175}{12})^{12(20)}}[/tex]
[tex]P = 56389[/tex]
He must deposit $56,389.
A similar problem is given at https://brainly.com/question/25263233
