Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

Find the future value and interest earned if $8704.56 is invested for 8 years at 4% compounded (a) semiannually and (b) continuously.
intorntic compounded semiannually is approximately


Sagot :

a) The future value, principal plus interest, with compound interest on a principal of $8,704.56 at a rate of 4% per year compounded 2 times per year over 8 years is $11,949.50.

b) The future value, principal plus interest, with compound interest on a principal of $8,704.56 at a rate of 4% per year compounded continuously over 8 years is $11,987.29.

How is the future value determined?

The future value can be determined using an online finance calculator.

Data and Calculations:

a) Compounded Semiannually:

Principal (P): $8,704.56

Annual Rate (R): 4%

Compound (n): Compounding Semi-Annually

Time (t in years): 8 years

Result:

A = $11,949.50

A = P + I where

P (principal) = $8,704.56

I (interest) = $3,244.94

Calculation Steps:

First, convert R as a percent to r as a decimal

r = R/100

r = 4/100

r = 0.04 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 8,704.56(1 + 0.04/2)(2)(8)

A = 8,704.56(1 + 0.02)(16)

A = $11,949.50

b) Compounded Continuously:

Using the formula A = Pert

Principal (P):  $8,704.56

Annual Rate (R): 4%

Compound (n): Compounding Continuously

Time (t in years):   8 years

Result:

A = $11,987.29

A = P + I where

P (principal) = $8,704.56

I (interest) = $3,282.73

Calculation Steps:

First, convert R as a percent to r as a decimal

r = R/100

r = 4/100

r = 0.04 rate per year,

Then solve the equation for A, using the mathematical constant, e = 2.71828

A = Pert

A = 8,704.56(2.71828)(0.04)(8)

A = $11,987.29

Thus, while the future value of $8,704.56 at a rate of 4% per year compounded semiannually over 8 years is $11,949.50,  the future value of $8,704.56 at a rate of 4% per year compounded continuously over 8 years is $11,987.29.

Learn more about compounding interest at https://brainly.com/question/24274034

#SPJ1