Question

1. Effects of different compounding periods on future values of $1,000 invested at an 8% nominal interest rate. Initial Amount Compounding periods Effective annual rate FV at end of 1 year $1,000 Annually $1,000 Semiannually $1,000 Quarterly $1,000 Monthly $1,000 Daily (365 days) 2. To illustrate with the simplest case of annual payments, suppose you borrow $22,000 at 12 percent compound annual interest to be repaid over the next six years. Equal installment payments are required at the end of each year. In addition, these payments must be sufficient in amount to repay the $22,000 together with providing the lender with a 12 percent return. Please determine the annual payment, and amortization schedule. 3. On Jan 1st, 2000 The real risk-free rate is 2% and is expected to be constant for next 20 years. Inflation is expected to be 7% next year, 5% the following year, and 3% thereafter. The maturity risk premium is estimated to be 0.2*(t-1) % and up to 1%. (t = number of years to maturity). 1) Please estimate the term structure of US treasury. 2) Draw the yield curve on Jan 1st, 2000 and what's the expected yield curve on Corporate bond?

Answer 1

Answer to Q#1 (First question in the list): Future Value in 1 year = Initial Investment x (1 + Effective Annual Rate) Initial Amount $1,000 $1,000 $1,000 $1,000 $1,000 Compounding Period Annually Semiannually Quarterly Monthly Daily (365 days) Effective FV at the Annual Rate end of 1 yr 8.0000% $1,080.00 ($1000 x (1 + 8.0000%)] 8.1600% $1,081.60 ($1000 x (1 + 8.1600%)] 8.2432% $1,082.43 ($1000 x (1 + 8.2432%)] 8.3000% $1,083.00 [$1000 x (1 + 8.3000%)] 8.3278% $1,083.28 ($1000 x (1 +8.3278%)] Workings: When compounded periodically, effective annual interest rate = (1 + Annual interest rate/# of periods per year)* or pe barvoar # of periods per year 1 Therefore, Annually Semiannually Quarterly Monthly Daily Annual interest rate 8% 8% 8% 8% 8% # of periods in a year 2 4 12 365 Effective annual interest rate 8.0000% 8.1600% 8.2432% 8.3000% 8.3278% [Ref: NOTE]

NOTE: Effective annual rate when compounded Annually: ((1+8%/1)^1) - 1 = ((1+8%)^1) - 1 = 8.0000% Effective annual rate when compounded Semiannually: ((1+8%/2)^2) - 1 = ((1+4%)^2) - 1 = 8.1600% Effective annual rate when compounded Quarterly: ((1+8%/4)^4) - 1 = ((1+2%)^4) - 1 = 8.2432% Effective annual rate when compounded Monthly: ((1+8%/12)^12) - 1 = ((1+0.67%)^12) - 1 = 8.3000% Effective annual rate when compounded Daily: ((1+8%/365)^365) - 1 = ((1+0.02%)^365) - 1 = 8.3278%