Start with a riskless zero coupon bond. Since there are no coupons there is this natural pull to par which is given by the simple formula Price = Par*E^(-rate *Time). The pull to par is not linear (as you suggested) but the exponential given.
Now if the bond has default risk the pull to par is more complicated because there is the whole issue of whether or not it is going to pay off at maturity. One way to look at that would be to say the bond simple has a different interest rate that reflects default probability and call that rate1 and then we have essentially the same formula with a pull to par Price = Par*E^(-rate1 *Time), again an exponential.
In the real world things are not so nice because default has a tenor and the uncertainty surrounding default diminishes as the bond gets closer to maturity. The rattiest corporate bond that anybody can actually issue has little probability of default in the first year or so. If the company has such liquidity problems that they won't be able to make coupon payments in the first year, nobody will underwrite the bond offering. Altman has lots of studies on default tenor and it seems that 3 years or so after issuance is when default probabilities really pick up.
Then fast forward to maturity minus a year or two. At this time, it is usually fairly clear if the company is going to be able to payoff the bond at maturity (obviously not always the case). The less uncertainty there is the more the bond starts following the simple exponential pull to [something] given above. If it is certain the bond will pay-off , the [something] is par. If it is certain the bond won't pay off the the [something] is an expected recovery on the bond perhaps discounted by the time until recovery.
This tenor of default has tons of mathematical models, starting with Markov chain models which are not too hard to understand. Note that sometimes you can directly observe market estimates of default tenor by looking at pricing of various credit default swaps of different tenors. If all you care about is default and risk-free interest rate, you can theoretically take credit default swaps pricing and treasury rates and draw a nice graph of the pull to par at any point in a bond's life. It won't be right because there are other issues in bonds like liquidity, optionality, recovery, and others but it is some starting point.
In any event, this is a central question in any bond analytics and you can literally make a career out of doing this for various bonds.
The movement of a bond's price toward its face value as it approaches its maturity date. Is there a general rule, when this effect starts? I thought, the effect can only be seen one year beforemarturity?
Is there a calculation method or is it just linear today-to-maturity?
