**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.