Respuesta :
Using the formula for compounded interest, it is found that an interest rate of 1.56% would be required.
------------------------
The compound interest formula is given by:
[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.
- Invest $11,000, thus [tex]P = 11000[/tex]
- 16 years, thus [tex]t = 16[/tex]
- End up with $14,000, thus [tex]A(t) = 14000[/tex]
- Compounded monthly, thus [tex]n = 12[/tex].
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]14000 = 11000(1 + \frac{r}{12})^{12(16)}[/tex]
[tex](1 + \frac{r}{12})^{192} = \frac{14}{11}[/tex]
[tex]\sqrt[192]{(1 + \frac{r}{12})^{192}} = \sqrt[192]{\frac{14}{11}}[/tex]
[tex]1 + \frac{r}{12} = (\frac{14}{11})^{\frac{1}{192}}[/tex]
[tex]1 + \frac{r}{12} = 1.0013[/tex]
[tex]\frac{r}{12} = 0.0013[/tex]
[tex]r = 0.0013(12)[/tex]
[tex]r = 0.0156[/tex]
An interest rate of 1.56% would be required.
A similar problem is given at https://brainly.com/question/23781391
