Problema Solution

find the accumulated value of an investment of $10,000 for 4 years at an interest rate of 5% if the money is a. compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously.

Answer provided by our tutors

Let

P = $10,000

t = 4 years

r = 0.05 or 5% annual interest rate

A = future value (accumulated value)

a. what is the accumulated value if the money is compounded semiannually?

n = 2

A=P(1+ r/n)^(nt)

A = 10000(1 + 0.05/2)^(2*4)

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click here to see the calculation for A

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A = $12,184.03

b. What is the accumulated value if the money is compounded quarterly?

n = 4

A=P(1+ r/n)^(nt)

A = 10000(1 + 0.05/4)^(4*4)

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click here to see the calculation for A

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A = $12,198.90

c. What is the accumulated value if the money is compounded monthly?

n = 12

A=P(1+ r/n)^(nt)

A = 10000(1 + 0.05/12)^(12*4)

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click here to see the calculation for A

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A = $12,208.96

d. What is the accumulated value if the money is compounded continuously? 

A=Pe^rt

A = 10000*e^(0.05*4)

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click here to see the calculation for A

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A = $12,214.03