Respuesta :
Answer:
a) The interest is compounded monthly, so should use the compound interest formula.
b) [tex]A(t) = 3000(1.0067)^{12t}[/tex]
c) Linda would have $14898.33 in her account after 20 years.
Step-by-step explanation:
Compound Interest Formula:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where 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 and t is the number of years for which the money is invested.
Continuous Interest Formula:
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(0) is the initial amount invested and r is the interest rate, as a decimal.
For Linda: a. State which formula should be used to solve this problem.
The interest is compounded monthly, so should use the compound interest formula.
b. Write the function for Linda.
Invests 3000, so [tex]P = 3000[/tex]
8% interest, so [tex]r = 0.08[/tex]
Compounded monthly. An year has 12 months, so [tex]n = 12[/tex]
Then
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A = 3000(1 + \frac{0.08}{12})^{12t}[/tex]
[tex]A = 3000(1.0067)^{12t}[/tex]
c. Determine how much Linda would have in her account after 20 years
This is A(20)
[tex]A = 3000(1.0067)^{12*20} = 14898.33[/tex]
Linda would have $14898.33 in her account after 20 years.
For Linda the formula that would be used to solve this problem is: FV = A (1 + r)^nm
For Linda, the function is: $3000(1.0067)^12n.
The amount Linda would have in her account after 20 years is $14,780.41.
The formula for determining the future value of an amount of money is: FV = A (1 + r)^nm
Where:
- FV = Future value
- A = Amount deposited
- R = interest rate = 8%/12 = 0.067
- m = number of compounding = 12
- N = number of years = 20
Value after 20 years $3000(1.0067)^(12 x 20) = $14,780.41.
A similar question was answered here: https://brainly.com/question/16035671
