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Interest rate calculator

Bond yield to maturity

Investment Resources
Ganesha's Financial Calculator
Be sure to enable JavaScript
Instructions: enter the known or given value (P, F, or A), i, and N, and click the button for the desired answer. Entries must be numerical. 
Each function was checked against a table of interest factors, and each seems to work correctly.
Present value P $ Future value of P given i, N
Future value F $ Present value of F given i, N
Annual (or monthly) payment A $ Capital recovery factor: A given P, i, N 
E.g. monthly mortgage payments if you borrow P dollars at monthly interest rate i%, to be paid off over N months.
Interest i, expressed as percent (0.10 = 10%) per month, year, etc. (see N) % Present value of a uniform series, P given A, i, N 
E.g. the true payoff of a "million dollar state lottery" that pays $50,000 per year for 20 years, if you can earn i percent on your investment.
Periods (months or years) N Sinking fund factor, A given F, i, N 
E.g. annual payments (investments) needed to have F dollars after N years, if the investment pays i% per year.
    Future value of a uniform series, F given A, i, N. 
E.g.future value of a retirement plan if one invests A dollars per year for N years at annual interest rate i. 

See why Social Security is a criminally fraudulent pyramid scheme. Enter your annual social security tax as A, years to retirement as N, and a reasonable investment return for i. This is what you should have when you retire, e.g. in an IRA or a Roth IRA. Let's see the government match that performance. (And remember, your employer matches your "contribution.")
    Reference: Riggs, James L. 1977. Engineering Economics. New York: McGraw-Hill
     

    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?
      Face value of the car loan or mortgage. (If the mortgage lender charges "points," or a loan origination fee, enter the remaining amount.) P $
      Periodic (usually monthly) payment
      Periods (usually months) to pay off the loan
      This is your loan's true interest rate %
      If the above is a monthly rate, this is your annual compounded 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: McGraw-Hill, 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:
    1. 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).
    2. 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.


    Present worth of N interest payments, adjusted for the time to the next payment. The present worth of a uniform series of N payments assumes that the first payment occurs one full period (usually a year) from now. But if the next payment is in half a year (for example), it should be multiplied by F/P(i,0.5) to move it to time zero. 
    P/A(i,N) = present worth factor for a uniform series of N payments given rate of return i. ("A" means annual, although the payments could be quarterly, monthly, etc.) 
    F/P(i,N) = future value factor    		 Present worth of the face value, which will be paid N+x-1 periods from now. 
    P/F(i,N) is the present worth factor, given rate of return i and time N.     		 Present cost of the bond. When i is correct, the expression sums to zero.
    C*(P/A(i,N))*(F/P(i,1-x)) +1000(P/F(i,N+x-1)) -P
       
    Cost of the bond P (example: if the price is 95 3/4, the bond costs $957.50 and is redeemed for $1000.00 at maturity.)
    		 $
    Coupon interest rate, % %
    Periods (coupon payments) to maturity N
    Periods to next coupon payment. For example, if the bond pays annually in December, and it is June, there is 0.5 period (year) to the next coupon. Must be between 0 and 1 (less than 1) to avoid computational error.
    Yield to maturity %

 
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)
    1. 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%.
    2. 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%.
    3. 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%.
    4. 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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