. 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:

Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Rate r s r r s r r s r r s r

1. (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?

2. (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.

3. (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 Month Rate Nov 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 Month Rate Nov 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