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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 :

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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

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