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An investor wants to analyze the earnings of a mutual fund account. Three years ago, the value of the account was $36,000 and it is now worth $50,400. If the account is compared to a bank account paying interest that is compounded continuously, what interest rate rounded to the nearest hundredth of a percent would the bank account have to pay to match the mutual fund account’s earnings? (Assume the only deposit was to open the account.)
R=14.346?

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An investor wants to analyze the earnings of a mutual fund account. Three years ago, the value of the account was $36,000 and it is now worth $50,400. If the account is compared to a bank account paying interest that is compounded continuously, what interest rate rounded to the nearest hundredth of a percent would the bank account have to pay to match the mutual fund account’s earnings? (Assume the only deposit was to open the account.) 
R=14.346?

anonymous · Answer

Continuously compounded means that the interest for an account is being calculated and applied constantly. The basic formula for continuously compounded interest is A=P*e^(r*t).
Where P is the principle invested, e is the exponential function, r is the interest rate, t is the time period of investment, and A is the total amount after time t.

So, in your question, 50400 = 36000*e^(3r)

e^(3r) = 50400/36000
3r = ln(50400/36000)
r = (ln(50400/36000))/3

Which works out to about 11.2%, so your R wouldn't work.