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nekit [7.7K]
3 years ago
5

Find the accumulated value of an investment of $ 20 comma 000 for 5 years at an interest rate of 6.5 % if the money is a. compou

nded​ semiannually; b. compounded​ quarterly; c. compounded monthly d. compounded continuously.
Business
2 answers:
marishachu [46]3 years ago
7 0

Answer:

A) $27,537.89

B) $27,608.40

C) $27,656.90

D) $27,680.61

Explanation:

present value = $20,000

n = 10 , 20 , 60

i = 3.25% , 1.625% , 0.5417%

a. compounded​ semiannually;

future value = $20,000 x 1.0325¹⁰ = $27,537.89

b. compounded​ quarterly;

future value = $20,000 x 1.01625²⁰ = $27,608.40

c. compounded monthly

future value = $20,000 x 1.005417⁶⁰ = $27,656.90

d. compounded continuously.

A = Peˣⁿ

where:

  • A = future value = ?
  • P = principal = $20,000
  • e = mathematical constant = 2.71828
  • x = interest rate = 6.5% = 0.065
  • n = periods = 5 years

A = $20,000 x 2.71828⁰°⁰⁶⁵ˣ⁵ = $20,000 x 2.71828⁰°³²⁵ = $20,000 x 1.384 = $27,680.61

AnnyKZ [126]3 years ago
5 0

Answer:

a. $27,538

b. $27,608

c. $27,662

d. $54,366

Explanation:

Future value of the investment is the sum of principal value and interest value including its compounding effect.

Use following formula of FV to calculate the Value of Investment.

FV = PV x ( 1 + r )^n

As per given data

PV = $20,000

Number of years = 5 years

r = 6.5%

FV = ?

a. compounded​ semiannually

n = 5 x 2 = 10 compounding periods

r = 6.5% / 2 = 3.25%

FV = $20,000 x ( 1 + 3.25% )^10 = $27,538

b. compounded​ quarterly

n = 5 x 4 = 20 compounding periods

r = 6.5% / 4 = 1.625%

FV = $20,000 x ( 1 + 1.625% )^20 = $27,608

c. compounded monthly

n = 5 x 12 = 60 compounding periods

r = 6.5% / 12 = 0.542%

FV = $20,000 x ( 1 + 0.542% )^60 = $27,662

d. compounded continuously.

FV   =   Pe^Yr = $20,000 x 2.71828 = $54,366

2.71828 is a constant value for continuous compounding

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Explanation:

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Consider a portfolio of stocks X, Y, Z whose returns in various economic conditions are set forth below.
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Answer:

The expected return is 10.95%

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CALCULATE THE EXPECTED RETURN OF X

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Boom ____ 0.25 ______22%  ___5.50%

Normal ___ 0.60 ______15%  ___ 9.00%

Recession _0.15 _______5% ___ <u>0.75%  </u>

Total ______________________<u>15.25%</u>

CALCULATE THE EXPECTED RETURN OF Y

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Boom ____ 0.25 ______10%  ___ 2.50%

Normal ___ 0.60 ______9%  ____5.40%

Recession _0.15 _______8% ___ <u>1.20%  </u>

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