Bank MakeMeRich holds a portfolio of mortgages. These mortgages have a maturity of 30-years, and a total value of $200 million with a coupon of 10 percent per year, which is paid quarterly. Using the annuity formula, the bank calculates that the quarterly mortgage payment equals $5,272,358.

Answer the following questions:

1) What are the interest and principal repayments, respectively, during the first quarter of the life of this mortgage portfolio? (5 points)

2) The bank constructed acollateralized-mortgage-obligation(CMO) using this mortgage pool as collateral. The CMO has three tranches. Tranche A has the highest seniority. Tranche B has the middle seniority. Tranche C has the lowest seniority. Tranche A has a value of $50 million and receives quarterly payments at 9 percent per year. Tranche B has a value of $100 million and receives quarterly payments at 10 percent per year. Tranche C has a value of $50 million receives quarterly payments at 11 percent per year.

Derive the payment schedule of Tranche A for the first 3 quarters, and the payment schedule of Tranche B for the first 2 quarters, by filling in the numbered table cells below (15 cells in total).

Instruction: Write down your equations deriving each of the 15 table cells. Number each equation corresponding to its cell number. You will receive ZERO credits if you don't write down the detailed derivation equations. (20 points).

Tranche A

Quarter

Beginning

Balance

Total

Payment

Interest

Payment

Principal

Payment

Remaining

Balance

1

(1)

(2)

(3)

(4)

(5)

2

(6)

(7)

(8)

3

(9)

(10)

Tranche B

Quarter

Beginning

Balance

Total

Payment

Interest

Payment

Principal

Payment

Remaining

Balance

1

(11)

(12)

(13)

2

(14)

(15)