You can borrow $1 from bank and repay the loan in one payment after 1, 2, 3,
Question:
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)
- 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
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill