Question

According to treasurydirect.gov, 30-Year treasury bonds earning 2.375% interest were issued on 11/15/2019 (CUSIP 912810SK5). These treasury bonds were offered in multiples of $100 (par or face value). Also, according to treasurydirect.gov, treasury bonds pay interest on a semi-annual basis. a. Lets say that you bought one of these treasury bonds. Every time you received an interest payment from this bond, you placed it in a savings account earning a yearly nominal 2.375% interest rate compounded semi-annually. In 30 years, when the bond matures, how much money will you have in your savings account (including the par value of the bond)? b. Using the same interest rate as 1a, what is the present worth of the savings account from la? C. Recalculate la, but instead use a yearly nominal 2.430% interest rate compounded semi- annually? d. Using the same interest rate as 1c, what is the present worth of the savings account from 1c? e. Using treasurydirect.gov (navigation is difficult...start with "Treasury Marketable Securities") determine the selling price per $100 for CUSIP 912810SKS. f. Explain 1a-1em

Answer 1

Answered 4 sub questions as per HOMEWORKLIB RULES.

Given,

Face Value (FV) = $1,000 Coupon rate (R)= 2.375% . Term to maturity (n)= 30 years.

Frequency of interest payment= Semi annual. Hence number of interest payments a year (t) =2.

Amount of interest per half year per bond= FV*R/t = $100*2.375%/2 =$100*0.011875= $1.1875

(a) Interest rate on Savings account= 2.375%.

The periodical interest deposited in Savings Account will have a maturity value of $103.0541948 calculated as future value of annuity as follows:

Therefore, money available in Savings Account on maturity of one bond bond, along with the par value of bond

= $103.0541948+$100 = $203.0541948

(b) interest rate of 2.375% compounded semiannually, present worth of the balance in Savings Account is as follows

PV= FV/(1+R/2)^n Where FV= Future Value ($203.0541948, R= Interest Rate (2.375%) and n= number of compounding periods (30*2=60)

Hence, PV= $203.0541948/(1+2.375%/2)^60 = $203.0541948/1.011875^60

= $203.0541948/2.0305419=$100

(c)  Interest rate on Savings account= 2.430%.

The periodical interest deposited in Savings Account will have a maturity value of $103.9839075 calculated as future value of annuity as follows:

Therefore, money available in Savings Account on maturity of one bond bond, along with the par value of bond

=$103.9839075+$100 = $203.9839075

(d) Interest rate of 2.430% compounded semiannually, present worth (PV) of the balance in Savings Account is as follows

PV= FV/(1+R/2)^n Where FV= Future Value ($203.9839075, R= Interest Rate (2.430%) and n= number of compounding periods (30*2=60)

Hence PV= $203.9839075/(1+2.430%/2)^60 = $203.9839075/1.01215^60

= $203.9839075/2.063919559 = $98.83326441