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Question - Nanny Ogg has 15 children whose birthdays are exactly 21 days apart, evenly distributed over the year (starting on January 1). Nanny Ogg's magic savings account has a continuous compounding interest rate of 10%, Nanny Ogg would like to create a family trust to provide $1000 to each of her children on their respective birthdays every year. In the next steps, we will find how much money Nanny Ogg has to deposit to endow the family trust.
(a) Find the effective annual interest rate.
(b) Find the effective 1/15-yearly interest rate.
(c) Find the present, value as of January 1 of a given year, of the birthday gifts paid out that year.
(d) Find how much money Nanny Ogg needs to endow the trust fund on January 1 of the year that the trust is established.
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