Try It Yourself#
Exercise 1#
If $6,000 is invested at \(7\%\) compounded continuously, what will be the accumulated amount after 6 years?
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Answer: \(A = 6000e^{0.42}\)
Exercise 2#
If $7,000 is invested at \(16\%\) compounded quarterly, what will be the accumulated amount after 3 years?
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Answer: \(A = 7000(1.04)^{12}\)
Exercise 3#
Find the interest rate \(r\) needed for an investment of $2,000 to grow to $8,000 in 7 years if compounded continuously.
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Answer: \(r = \ln(4)/7\)
Exercise 4#
Find the interest rate \(r\) needed for an investment of $7,000 to grow to $12,000 in 21 years if compounded monthly.
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Answer: \(r = 12\left[(12/7)^{1/252} - 1\right]\)
Exercise 5#
Find the time it would take for an investment of $1,000 to grow to $100,000 if interest is compounded quarterly at an annual rate of \(8\%\).
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Answer: \(t = \frac{\ln(100)}{4\ln(1.02)}\)
Exercise 6#
Find the time it would take for an investment of $2,500 to grow to $6,000 if interest is compounded continuously at an annual rate of \(24\%\).
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Answer: \(t = \frac{25}{6}\ln(12/5)\)
Exercise 7#
Calculate the effective rate of interest corresponding to a nominal interest rate of \(52\%\) compounded weekly.
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Answer: \(r_{eff} = 1.01^{52} - 1\)
Exercise 8#
Your grandma would like to establish a trust fund for your education. How much should she set aside now if she wants $50,000 in 9 years and interest is compounded monthly at an annual rate of \(12\%\)?
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Answer: \(P = 50000(1.01)^{-108}\)
Exercise 9#
You are preparing to run for president and want to have $100,000 in 6 years to start your campaign. How much money do you need now if interest is compounded continuously at an annual rate of 15%?
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Answer: \(P = 100000e^{-0.9}\)
Exercise 10#
You have $50,000 in the bank earning \(7\%\) interest compounded quarterly. However, your cousin needs a $50,000 investment to start up his new financial consulting business. In order to get the same total return as leaving your money in the bank, what interest rate \(r\) should you request from your cousin if interest is compounded continuously?
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Answer: \(r = 4\ln(1+0.07/4)\)