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On January 1, 2017, Smith deposits 1,000 into an account earning nominal annual interest rate of...

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Advance Math

On January 1, 2017, Smith deposits 1,000 into an account earningnominal annual interest rate of i(4) = 0.04 compounded quarterlywith inter- est credited on the last day of March, June, September,and December. If Smith closes the account during the year, simpleinterest of 4% is paid on the balance from the most recent interestcredit date.

(a) What is Smith’s close-out balance on September 23, 2017?

(b) Suppose all four quarters in the year are considered equal,and time is measured in years. Derive expressions for Smith’saccumulated amount func- tion A(t), the close-out balance at timet. Consider separately the four inter- vals 0 ? t ? 0.25, 0.25 ? t? 0.50, 0.50 ? t ? 0.75 and 0.75 ? t ? 1 and draw the time diagramfor each of these cases.

(c) Using part (b), show that if 0 ? t ? 0.25, then it followsthat ?t = ?t+0.25 = ?t+0.50 = ?t+0.75.

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