You can borrow $1 from bank and repay the loan in one payment after 1, 2, 3, etc.  —your choice.  Repayment amounts --see Table 1  (E.g., if you borrow $1 for 17 Years ,you repay $4.5 after 17 years)

1. Calculate the annual  and semi-annual  compounding interest rates on these loans. They are called   zero-coupon rates or spot rates because loans repayments have no intermediate payments ["coupons"]; only one cash flow at the end of the loan.

Aside: for one-year the loan rate is 5%; for two-year loan rate is calculated from  ; 

For three-year loan rate is calculated from  ; Etc. 

Table 1

maturity of $1 loan	Paying back after N Years
1	1.05
2	1.12
3	1.20
4	1.30
5	1.44
6	1.62
7	1.81
8	1.9
9	1.99
10	2.07
11	2.22
12	2.41
13	2.65
14	2.9
15	3.3
16	4
17	4.5
18	5.2
19	6
20	7

Build an Excel spreadsheet that calculates this type of zero-coupon rates (annual compounding) and apply it to the data of zero-coupon loans with 1-20 Years. 

  Graph the Annual and S/A rates: x axes- years, y axes rates. 

The curve is called the spot yield curve or the zero-coupon yield curve.

Using rates from above, price a bond that has Face Value of $100, pays a $20 annual coupon [first coupon payment in a year from today] and matures 4 years from today