Mortgage / Bond Calculator

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 Present Value discounted at rate R = Periodic Payments of amount A for N periods + Final Payment of amount B at period N Start of Period Payments End of Period Payments

Introduction

This calculator determines the present value for mortgages, pure discount bonds, and coupon bonds,  It will also calculate the rate of return (or bond yield-to-maturity) that makes the present value equal to a known market price for the security.

Buttons: PV | R | A | B

Click any one of these buttons to calculate the associated parameter given the values of the other three parameters.  The discount rate R is stated in percentage points so that 5.0 = 5%.

Button: N

The N button enters N, but recalculates the present value PV. That is, you can set N to any positive value, but this calculator does not solve for N.  There is a limit of 1000 periods.

TABLE | TEXT

The table shows how a bank account at rate R  with beginning balance PV could replicate the income stream specified by A, B, and N.  The TABLE suppresses this text in order to produce a nicer printout.  The TEXT button restores this text after you produce a table.

If you would like to make a printed copy of your calculations or save them to a file, the "File" menu heading for your browser probably contains "Print" and "Save As" options.

Security Types

For a pure discount (zero coupon) bond, the periodic payment A is zero.  For a mortgage, the final payment B is zero.  For a coupon bond, the periodic payment A is the coupon rate times the principal and the final payment B is the principal.

To compute the present value of a fixed-income security, the discount rate R should be the current discount rate, but the periodic payments and final payment should stay fixed at the original values.  For example, the present value of a \$1000 bond with a 10% coupon rate (and \$100 periodic payments) is \$1000 if the discount rate is 10%.  Changing the discount rate to 8% changes the present value of the same payment stream to \$1,225.16.

To calculate the original payment amount for a fixed-rate mortgage, set PV to the loan amount, set R to the contract interest rate, set N, and then click A.

Note

It is possible to enter values that create impossible calculations.  For example, a pure discount bond that costs \$1000 and returns \$900 after one year has a negative yield R.  A lower bound of zero is imposed to eliminate the possibility of calculating negative interest rates. In general, entering impossible numbers will leave the other parameters unchanged after a button is clicked.