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you deposit $750 in a savings account the earns a 5% annual interest compounded quarterly.

a. write the function that represents the balance after t years.

b. what is the balance of the account after 4 years?​

Respuesta :

samuelonum1

Answer:

a. [tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

b .$914.85

Step-by-step explanation:

Step one:

given data

principal p=$750

rate= 5%= 0.05

for quarterly compounding n=4

a. the function that represents the balance after t years.

[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

b. when t=4

[tex]A = 750(1 + \frac{0.05}{4})^{4*4}\\\\A= 750(1 +0.0125)^{16}\\\\A= 75(1.0125)^{16}\\\\A= 750*1.2198\\\\A=914.85[/tex]

A= $914.85

The function that represents the balance after t years is FV = $750( 1.0125)^4t.

The balance of the account after four years is $914.92.

What is the function that represents the balance after t years?

The formula for calculating future value:

FV = P (1 + r)^nm

Where:

  • FV = Future value
  • P = Present value
  • R = interest rate = 5%/4 = 1.25%
  • m = number of compounding = 4
  • N = number of years

FV = $750( 1.0125)^4t

What is the account balance after 4 years?

$750( 1.0125)^(4 x 4) = $914.92

To learn more about future value, please check: https://brainly.com/question/18760477

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