Question

Suppose that you invest in a two-year Treasury bond with a coupon rate of 6% and $1,000 par. Suppose that you buy this bond at a price of exactly $1,000. You intend to hold this bond to maturity and reinvest the coupons until the bond matures. You expect to reinvest the coupons in an account that pays an APR of 2.83%, with semi-annual compounding. What is the effective annual rate of return on your investment?

Answer 1

Since it is a Treasury bond, it is assumed that interest is paid semi annually.

Given,

Face Value of Bond (F) = $1,000. Term to maturity= 2 years.

Coupon Rate= 6% Therefore, Semi annual interest= $1,000*6%/2 = $30

The cash flows comprising the interest payments constitute an annuity at 2.83% interest (APR). Future value of the interest payments= $ 122.57 Calculated as follows:

F A B C D | | Ε G 1 Future Value of Annuity Payments at the end of each period 2 3 Future value of annuity is calculated using the formula FVA= P*{[(1+r)^n]-1/r] 4 Where P= Periodical payments, 5 n= Number of payments. Eg. if number of years=N, then n=N*2 for semi annual payments 6 r= Rate of interest per period in decimals 7 All amounts in $ Given that 9 Periodical payments (P)= 30 No. of years (N)= 10 Rate of interest (% p.a)=R= 2.83 No. of payments a year (t)= 11 12 Calculations: 13 Formula Cell reference Value 14 Interest rate per period in decimals (r )= R/(100*t) D10/(100*G10) 0.01415 15 No. of periods (n)= N*t G9*G10 16 (1+r)= 1+G14 1.01415 17 (1+r)^n= G164G15 1.05781271 18 [(1+r)^n)-1= G17-1 0.05781271 19 [(1+r)^n]-1/r= G18/614 4.08570372 20 Future value of annuity FVA= P*{[(1+r)^n)-1/r} D9*619 122.571112 21 Rounded to $122.57 22

Total amount on redemption= Face Value + Future Value of interest stream

=$1,000 + $122.57 (FV)= $1,122.57

Purchase price (P)= $1,000

Effective annual rate of return=[(FV/P)^(1/n)]-1

Where FV= Total amount receivable on maturity, P= Purchase price and n= period of holding (number of years given as 2)

Substituting the values,

Effective annual rate of return= [(1,122.57/1,000)^(1/2)]-1 = 1.05951404 -1 = 5.951404%