Question

The principal amount, $5500, earns 3.75% interest compounded continuously.

Answer 1

Answer:

a)

The function that represents the value of the account at any time, t

$\:\:A=Pe^{rt}$

b)

The total amount accrued, principal plus interest,  from compound interest on an original principal of  $ 5,500.00 at a rate of 3.75% per year  compounded continuously  over 6 years is $ 6,887.77.

Step-by-step explanation:

a. Write the function that represents the value of the account at any time, t.

The function that represents the value of the account at any time, t

$\:\:A=Pe^{rt}$

where

A represents the Future Value

P represents the Principle (Initial Value)

r represents the Interest rate

t represents the time

b) What will the value be after 6 years?

Given

The principal amount  P = $5500

Annual Rate r = 3.75% = 3.75/100 = 0.0375

Time Period  t  = 6 years

To Determine:

The total amount A = ?

Using the formula

$\:\:A=Pe^{rt}$

substituting the values

$A\:=\:5500\left(2.71828\right)^{\left(0.0375\right)\left(6\right)}$

$A=5500\cdot \:2.71828^{0.225}$

$A = 6,887.77$ $

Therefore, the total amount accrued, principal plus interest,  from compound interest on an original principal of  $ 5,500.00 at a rate of 3.75% per year  compounded continuously  over 6 years is $ 6,887.77.