(Continuous compounding, 11) Suppose you have $1 million and you can invest

it in a bank account that pays interests at an annual percentage rate (APR) of 3%. You want

to invest your $1m for 5 years.

(a). Suppose you are allowed to reinvest the interest at the end of every year (i.e., annual

compounding). What is the balance of your account at the end of year 5? (2)

(b). Suppose you are allowed to reinvest the interest at the end of every month (i.e., monthly

compounding). What is the balance of your account at the end of year 5? (2)

(c). Suppose you are allowed to reinvest the interest at the end of every day (i.e., daily

compounding). What is the balance of your account at the end of year 5? (Assume there are

365 days in a year.) (2)

(d). Suppose you are allowed to reinvest the interest at the end of every hour (i.e., hourly

compounding). What is the balance of your account at the end of year 5? (Assume there are

365 days in a year and 24 hours in a day.) (2)

(e). The formula of continuous compounding is

lim (1 +

)

=

,

where denotes the compounding frequency and is the number of years. Use the

formula of continuous compounding to calculate the balance of your account at the end of

year 5. Compare the answers in (a)-(e). What do you conclude? (3)