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Find the accumulated value of an investment of $ 15,000 for 5 years at an interest rate of 5.5 %if the money is
a. compounded​ semiannually;
b. pounded​ quarterly;
c. pounded monthly
d. compounded continuously.

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thuyntd

Answer:

The accumulated value of the investment after 5 years is

a. Compounded semiannually: $19,675

b. Compounded quarterly: $19,711

c. Compounded semiannually: $19,735

d. Compounded continuously: $19,747

Explanation:

Formula for a. b. c. : Future Value (FV) = [tex]PV \times [1 + (i/n)]^{n\times t}[/tex]

Formula for c: FV = [tex]PV \times e^{i\times t}[/tex]

Where:

  • PV = present value of the deposit/investment ($15,000)
  • i = stated interest rate (5.5%)
  • n = number of periods in a year
  • t = number of years (5)

a. Compounded semiannually: n=2 => FV = 15,000 * [1+(5.5%/2)]^(2*5) = $19,675

b. Compounded quarterly: n=4 => FV = 15,000 * [1+(5.5%/4)]^(4*5) = $19,711

c. Compounded semiannually: n=12 => FV = 15,000 * [1+(5.5%/12)]^(12*5) = $19,735

d. Compounded continuously: FV = 15,000 * e^(5.5%*5) = $19,747

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