Using compound interest, it is found that Melanie would need to invest a value of $7,710.
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]
- 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, we have that:
- Rate of 3.1%, hence [tex]r = 0.031[/tex].
- Compounded daily, hence [tex]n = 365[/tex].
- Value of $11,900 in 14 years, hence [tex]t = 14, A(t) = 11900[/tex].
- The amount she needs to invest is P.
Hence:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]11900 = P\left(1 + \frac{0.031}{365}\right)^{365(14)}[/tex]
[tex]1.54339P = 11900[/tex]
[tex]P = \frac{11900}{1.54339}[/tex]
[tex]P = 7710[/tex]
Melanie would need to invest a value of $7,710.
To learn more about compound interest, you can take a look at https://brainly.com/question/25781328
