koch@chopin.DEC (Kevin Koch LTN1-2/B17 DTN229-6274) (04/14/85)
> > There are five different bonds which each cost $2,000.00. > > Maturity of the five bonds is as follows: > > > > 7 years $ 4,000.00 > > 10 years $ 6,000.00 > > 15 years $ 10,000.00 > > 21 years $ 20,000.00 > > 29 years $ 50,000.00 > > > > Is there any way to figure out the actual interest rate that > > each bond is receiving. I am sending for more information today, > > but until I receive it, I though I would solicit information from > > the net. > > Figuring out the actual interest rate is relatively easy. In the > following formulas, these variables mean: > N : number of years to maturity > V : value of bond at maturity > C : initial cost of bond > i : interest rate > e : 2.71828... (the natural number) (not a variable, actually.) > > From the definition of compound interest: > > C * (1 + i)^N = V > > Solving this equation for i: > > i = e^(1/N * ln(V/C)) - 1 > > That wasn't so hard, now, was it? The quick and dirty method is to use the rule-of-72. Conveniently, the 7 year bond matures at exactly double the purchase price, so the yield is 72/7 = 10.29%. Its also obvious that the yield curve is back to normal -- long term investments paying higher yields. If the yield on the 21 year bond were also 10.29%, the bond would mature at $16000 (the value doubles every seven years). You can also see the yield going up on the longer term bonds by noting that the doubling time goes from 7 years (short term) to 6 years (15 years to 21 years). Note that neither the rule of 72 or the accurate formula stated above works when there is a coupon. The general yield-to-maturity calculation can only be done numerically.