Question

A young engineering company is a subcontractor in an effort to develop technology that will reliably detect and respond to release of a nuclear weapon. The company is in need of additional funding and issues a series of $1,000 face value bonds that pay a nominal annual rate of 6% with quarterly payments. The bond matures in 5 years.

If you buy one bond for $900, but need to sell it immediately after the 12^th interest payment for $900, what is your effective annual rate of return?

Answer 1

When compounded quarterly, Effective annual yield rate = (1 + quarterly interest rate)4 - 1 as there will be 4 quarterly compoundings per year. # of quarters to maturity, NPER Quarterly payment amount, PMT Bond's price today, PV Bond's selling price at the end, FV Quarterly coupon payment type, TYPE Weekly rate of interest earned Number of weeks per year Effective Annual Rate (EAR) 12 $15 ($1,000 x 6% / 4 --> Coupons are payable on par value at coupon rate] $900 $900 0 = 0 if paid at the end of each period; 1 if paid at the beginning of each period 1.6667% [Ref: EXCEL SCREENSHOT] 4 6.84% [((1+1.6667%)^4) - 1 = (1.01666714) - 1 = 0.0684 = 6.84%] EXCEL SCREENSHOT: Weekly rate of interest earned is calculated using EXCEL FUNCTION RATE(nper,pmt,pv,fv,type) where nper=12; pmt=-15; pv=900; fv=-900; type=0; Here, pmt & fv are negative as they denote cash inflows; pv is positive as it denotes cash outflow; type = 0 as coupons paid at the end of each period only. B с D E 12 =1000*6%/4 ($1,000 x 6%/4 --> Coupons are payable on par value at coupon rate) $900 A 1 # of quarters to maturity, NPER 2 Quarterly payment amount, PMT 3 Bond's price today, PV 4 Bond's selling price at the end, FV 5 Quarterly coupon payment type, TY 6 Weekly rate of interest earned 7 Number of weeks per year 8 Effective Annual Rate (EAR) $900 0 = 0 if paid at the end of each period; 1 if paid at the beginning of each period =RATE(B1,-B2,B3,-B4,B5) [Ref: EXCEL SCREENSHO = 0 if paid at the end of each period; 1 if paid at the beginning of each period. 4 [Ref: NOTE] =((1+B6)^B7)-1 [((1+1.6667%)^4) - 1 = (1.01666714) - 1 = 0.0684 = 6.84%]