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1. Suppose r,s > 0 are interest rates. You invest in an account which compounds at the end of each month according to the following schedule: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Month Rate Dec r S r r S r r S r r S r (i) If you invest P dollars into this account on January 1st, and this is the only deposit that you make, what is the value of the account after one year? (ii) Suppose you invest P dollars on January 1st of every year. What is the value of the annuity after n-years? Express your answer without using a sum. (iii) Suppose you invest P dollars on January 1st, April 1st, July 1st, and October 1st of each year. What is the value of the annuity after n-years? Express your answer without using a sum. 1. Suppose r,s > 0 are interest rates. You invest in an account which compounds at the end of each month according to the following schedule: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Month Rate Dec r S r r S r r S r r S r (i) If you invest P dollars into this account on January 1st, and this is the only deposit that you make, what is the value of the account after one year? (ii) Suppose you invest P dollars on January 1st of every year. What is the value of the annuity after n-years? Express your answer without using a sum. (iii) Suppose you invest P dollars on January 1st, April 1st, July 1st, and October 1st of each year. What is the value of the annuity after n-years? Express your answer without using a sum

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