Question

Suppose the term structure of​ risk-free interest rates is as shown​ below:

Term	1 yr	2 yr	3 yr	5 yr	7 yr	10 yr	20 yr
Rate​ (EAR ​%​)	1.92	2.35	2.61	3.22	3.85	4.39	5.09

a. Calculate the present value of an investment that pays

$1,000

in two years and

$4,000

in five years for certain.

b. Calculate the present value of receiving

$100

per​ year, with​ certainty, at the end of the next five years. To find the rates for the missing years in the​ table, linearly interpolate between the years for which you do know the rates. ​ (For example, the rate in year 4 would be the average rate in year 3 and year​ 5.)

c. Calculate the present value of receiving

$1,900

per​ year, with​ certainty, for the next 20 years. Infer rates for the missing years using linear interpolation. ​ (Hint: Use a​ spreadsheet.)

PLEASE SHOW SPREADSHEET FORMULA FOR ANSWER C ONLY - ALREADY FIGURED OUT A AND B

Answer 1

PV of cash Flow of $1900 per year = $24979

Interest rate for year 11 = [Year 10 interest rate * (20 - Current Year) / 10] + [Year 20 interest rate * (Current Year - 10) / 10]

Interest rate for year 11 = [Year 10 interest rate * (20 - 11) / 10] + [Year 20 interest rate * (11 - 10) / 10]

Interest rate for year 11 = [4.39% * (20 - 11) / 10] + [5.09% * (11 - 10) / 10]

Interest rate for year 11 = 4.46%

The same formula follows for the other years