Question

1.) You are examining treasury securities over a two-year horizon. Assume the annual real risk-free rate of interest (r*) is constant at 2%. The inflation rate is expected to be 3% for next year and 5% the following year. Assume the maturity premium is 2% for a two-year bond. Given these factors, what would be the interest rate on a two-year treasury security?

2.) You just took out a 5-year loan for $10,000 with an annual interest rate of 5%. At the end of the first year, what will be the ending balance on your amortized loan?

Answer 1

(1) Risk - free rate of interest = 2 %

inflation rate in year 1 = 3%

inflation rate in year 2 = 5 %

therefore Risk free rate of interest in year 1 = 2% + 3% = 2.06 %

and risk free rate of interest in year 2 = 2% + 5 % = 2.10 %

2 year average of risk free rate of interest = (2.06 % + 2.10 % ) / 2 = 2.08 %

two year maturity premium = 2 %

Therefore interest rate on two year Tresury security = 2.08 % + 2% = 4.08 %

(2) Calculation of loan ending balance at year 1 end

loan amount = $ 10000

time period = 5 year

interest rate = 5%

installment of loan = $ 10000 / PVAF( 5 % , 5 year )

= $ 10000 / 4.3295

= $ 2310 ( round off)

first year interest on loan = $ 10000 * 5% = $ 500

net principal paid back = installment - interest = $ 2310 - $ 500 = $ 1810

amoritse balance at year 1 end = $ 10000 - $ 1810 =$ 8190  

at the end of year 1 balace of amoritse loan is $ 8190 .