Problema Solution
An investor wants to analyze the earnings of a mutual fund account.Four years ago the value of the account was $16,000 and it is now worth $24,000( no additional deposits were made). 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 accounts earnings?
Round the answer to the nearest hundredth of a percent.
Answer provided by our tutors
P = $16,000 the principal
t = 4 years
r = the annual interest rate
A = $24,000 the future value
the future value formula is:
A=Pe^(rt)
we plug the above values and get:
16,000*(e^(4r)) = 24,000
e^(4r) = 24,000/16,000
4r = ln (3/2)
r = (1/4)(ln(3/2))
r = 0.1014 or 10.14%
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the bank would have to pay 10.14% interest rate.