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.
The future value can be determined using an online finance calculator.
Data and Calculations:
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
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
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
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.
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