Question

You are given $67,556,416.88 to manage so that the fund will have at least $100,000,000 available in 2030, 10 years from now. The yield curve is flat, and the current interest rate for all maturities is 4%. The only bonds that you can buy are annual coupon Treasury bonds with 1-year maturities and bonds issued in 2020 that mature in 2040 (currently a maturity of 20 years). All bonds are issued at par.

1. How many of each Treasury bond should you buy today?  

$_________________1-Year

$_________________20-Year

2. If all interest rates increase by 1% (to 5%) in year (2021) and then remain at 5%, how much will the fund have in 2030? Reinvest all coupon payments in one-year bonds. (The answer should be fairly close to the goal amount if you selected the portfolio correctly. If you set up the Excel spreadsheet right, you can see that you will have the goal amount regardless of the new interest rate.)

$_______________________

1. Very briefly, why was the amount not equal to exactly $100,000,000? (I’m looking for a key word.)

Answer 1

1. Given yield curves are flat thus amount can be invested in either of the bonds.

2. Fund will have $108,993,956.88 by end of 10 years. The amount is dependent on the fact that fractional Bonds are not available and reinvestment can only be done in multiple of $1000

Coupon Rate	4%	5%	5%	5%	5%	5%	5%	5%	5%	5%
Coupon Amount	2702240	3512900	3688550	3873000	4066650	4269950	4483450	4707650	4943000	5190150
Maturity Amount										67556000
Reinvested Amount	2702000	3513000	3689000	3873000	4066000	4270000	4484000	4707000	4943000	5190000
Free Amount	416.88	656.88	556.88	106.88	106.88	756.88	706.88	156.88	806.88	806.88	956.88
Total Invested	67556000	70258000	73771000	77460000	81333000	85399000	89669000	94153000	98860000	103803000	108993000
Total Amount	67556416.88	70258657	73771557	77460107	81333107	85399757	89669707	94153157	98860807	103803806.9	$ 108,993,956.88
Year	0	1	2	3	4	5	6	7	8	9	10