Ma 113 Functions And Inverse Functions, The Exponential Function And The Logarithm Worksheet Page 38
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41where P (t) is the value at time t, A
is the initial investment, r is the interest rate, t is the time
0
in years, and n is the number of times compounded per year. Verify that
r
lim
(1 + hr)
= lim
1 +
n
0
1
(Hint: Use the change of variable h =
)
Use part (b) to derive a formula involving e for continuously compounded interest.
(Hint: How can you represent continuously compounded interest as a limit where the interval of
time between each compounding decreases to zero and the number of compoundings increases to
infinity?)
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