Question

On January 1, 2017, Smith deposits 1,000 into an account earning nominal annual interest rate of i(4) = 0.04 compounded quarterly with inter- est credited on the last day of March, June, September, and December. If Smith closes the account during the year, simple interest of 4% is paid on the balance from the most recent interest credit 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’s accumulated amount func- tion A(t), the close-out balance at time t. 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 diagram for each of these cases.

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

Answer 1

The solution of the above first problem is given below:

This is the required solution for the given first problem.