Question

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

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

b. What will the value be after 6 years?

Answer 1

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.

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.