Scheme RST

An interest rate of r > 0 is applied at the end of the first week,

An interest rate of s > 0 is applied at the end of the second week,

An interest rate of t > 0 is applied at the end of the third week. Thereafter, the cycle repeats, so that the rates r, s, and t are applied at the end of the

3. (i) Using Scheme RST you'd like to set up a three-year annuity where you are able to withdraw A dollars from an account at the end of each three week period. How much should your initial deposit be?

(ii) Compute your initial deposit if you'd like the annuity in (i) to instead be a perpetuity, so you can make withdrawals of A every three weeks indefinitely.