Answered

Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

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 :

anthougo

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

Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.