Interest rate calculator
Bond yield to maturity
Investment Resources


Ganesha's Financial Calculator
Be sure to enable JavaScript
Reference: Riggs, James L. 1977. Engineering Economics. New
York: McGrawHill
Mortgage and Car Loan Interest Rates
Is the car salesman lying to you about your car loan's interest rate? (I
never knew a car salesman to lie unless it was absolutely convenient...)
They usually tell you what the monthly payment is. Are you getting the
advertised interest rate?
Example: The monthly payment on a five year (60 month), $10,000 car
loan is $222.45. The algorithm solves for interest rate i in the expression
$222.45*P/A(i,N=60)  $10,000 = 0. That is, $222.45 times the capital recovery
factor must equal the loan's present value. The result is 1.00%, but this
is the monthly rate. The annual compounded rate is 1.01 to the 12th power,
minus one, = 12.68%.
Note: Per Riggs, James L. 1977. Engineering Economics. New York:
McGrawHill, the capital recovery factor for 1% interest, 60 periods, is
0.02225. That is, 60 payments of $222.5 at a 1% interest rate has a net
present value of $10,000.
Bond Yield to Maturity: Beta Version
Caution: Tests of this algorithm do not yield exactly the same
yields to maturity shown in the Wall Street Journal or Barrons'.
(See below for possible explanation: comments are welcome.)
Procedure:

Let the coupon payment be $1000 (bond face value) times the coupon interest
rate. The bond costs P dollars to buy today.

The bond will pay N interest payments to maturity.

There is (0<=x<1) period to the next interest payment. For example,
if the bond pays (and matures) on 12/31/2000, and today is 6/30/98, N=3
(12/31/98, 12/31/99, 12/31/00) and x is about 0.50 (half a year to the
next interest payment).

The JavaScript algorithm solves for the yield to maturity (i) by bisection
of the interest range 0.01 to 100 percent, to drive the following
expression to zero.
Examples. WSJ = Wall Street Journal, source The Bond
Buyer
Date, source 
Bond, Maturity 
Price 
Coupon % 
Calculated YTM 
Given YTM 
4/22/98 WSJ C15 
MTA NY, 4/01/2023 
95 3/4 
5.000 
5.33% (1) 5.31% 
5.30% 
4/22/98 WSJ C15 
NYS Dormitory Auth. 8/01/2032 
94 1/2 
5.000 
5.60% (2) 5.35% 
5.35% 
4/22/98 WSJ C15 
Treasury 3/31/3000 
99.27 * 
5.500 
5.751% (3) 5.585% 
5.584% 
4/6/98 Barrons MW59 
U.S. Zero Coupon, matures Nov. 2012 
43 1/32 
0 
5.95% (4) 5.78% 
5.86% 
* Source: Dow Jones. Reading the "fraction" as 32nds (99.27 = 99 27/32, i.e. $998.44 for the bond)

Using x=0.95 year. There are 25 payments to maturity, with 345 days (0.96
year) to the next payment. Using a full year (0.9999) to the next payment,
the result is 5.31%.

Using x=100/365 year = 0.274. There are 35 payments to maturity. Using a full year
(0.9999) to the next payment yields 5.35%.

Using x=345/365 year = 0.945. There are 2 payments (3/99 and 3/00) to maturity.
Using a full year (0.9999) to the next payment yields 5.585%.

Using x=7/12 year. To match the posted result, one must use 0.81 year (9.7
months) to the next "payment," but November (day unknown) must be less
than eight months in the future. Check: $1000 times (1.0586)^14.81 year
= $430.25 ~ $430.31 (43 1/32).
These results suggest that the algorithm used to compute the listed yield
assumes
that the next payment takes place in a year. Comments welcome!
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