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**Unformatted text preview: **ear) Case
A 50,000 12 6 3 C 1,000 5 1 10 D 4–34 $ 2,500 B LG5 Amount of
initial deposit Nominal
annual rate, i 20,000 16 4 181 6 6% Deposit period
(years) 2 5 Continuous compounding For each of the cases in the following table, find the
future value at the end of the deposit period, assuming that interest is compounded continuously at the given nominal annual rate. Case Amount of
initial deposit Nominal
annual rate, i A $1,000 B 600 C 4,000 8 7 D 2,500 12 4 9%
10 Deposit
period (years), n
2
10 LG5 4–35 Compounding frequency and future value You plan to invest $2,000 in an
individual retirement arrangement (IRA) today at a nominal annual rate of 8%,
which is expected to apply to all future years.
a. How much will you have in the account at the end of 10 years if interest is
compounded (1) annually? (2) semiannually? (3) daily (assume a 360-day
year)? (4) continuously?
b. What is the effective annual rate, EAR, for each compounding period in
part a?
c. How much greater will your IRA account balance be at the end of 10 years
if interest is compounded continuously rather than annually?
d. How does the compounding frequency affect the future value and effective
annual rate for a given deposit? Explain in terms of your findings in parts a...

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