Great Western Bank has offered a special certificate of deposit (CD) tied to the S\&P 500.

Funds are deposited into the account at the beginning of a month and are held in the account for 3 years. Interest is credited to the account at the end of each year, and the amount of interest paid is based on the performance of the S\&P 500 index during the previous 12 months. Specifically, \({ }^{6}\) at the end of the first year, if the value of the index at the end of \(k\) months is \(S_{k}, k=0,1,2, \ldots, 12\), the average of the 12-month index values is defined as \(A=\frac{1}{12} \sum_{k=1}^{12} S_{k}\) and the interest paid is

times the initial account balance. Interest in the following years is computed in the same fashion, with new values of account balance and index values. Assuming that monthly changes in the S\&P 500 index can be modeled as geometric Brownian motion with \(\sigma=.20\), what risk-free rate is equivalent to this CD? 

Transcribed Image Text:

Imax10, (A-So)/Sol