Time Value of Money is based on the premise that an investor prefers to receive a payment of a fixed amount of money today, rather than an equal amount in the future, all else being equal. All of the standard calculations are based on the most basic formula, the present value of a future sum, “discounted” to the present. For example, a sum of FV to be received in one year is discounted (at the appropriate rate of r) to give a sum of PV at present.

### TVM Keys Description:

[N] Stores or calculates the number of payments or compounding periods (N).

[xP/YR] Multiplies a value by the number of payments per year and stores as N.

[I/YR] Stores or calculates the nominal annual interest rate as a percentage.

[PV] Stores or calculates the present value (PV). To a lender or borrower, PV is the amount of a loan; to an investor, PV is the initial investment. PV always occurs at the beginning of

the first period.

[PMT] Stores or calculates the dollar amount of each periodic payment (PMT). Payments can occur at the beginning or end of each compounding period.

[P/YR] Stores or calculates the number of payments or compounding periods per year.

[FV] Stores or calculates the future value (FV), a final cash flow. FV always occurs at the end of the last compounding period.

[Beg] Sets Begin mode (Beg). Payments occur at the beginning of each compounding period.

[End] Sets End mode (End). Payments occur at the end of each compounding period.

Here is an example of solving TVM problem using HP 20b.

You borrow $1,400,000.00 from a bank for 30 years (360 months) at 6.5% annual interest, compounded monthly. What is your monthly payment to the credit union? Note: at the end of the 30 years, you expect to have a zero balance (FV=0). Set the HP 20b to RPN as the active operating mode.

The HP 20b Solution:

- 12 [Shift] [P/YR] This sets 12 as the current value for the number of payments, or compounding periods.
- 360 [N] Enter 360 as the current value for the number of payments over 30 years.
- 6.5 [I/YR] Enter 6.5 as the current value for the interest rate percentage per year.
- 1400000 [PV] Enter the present value of the loan at the time of the first payment. This value is positive (+); it is money you receive.
- 0 [FV] Enter the future value of the loan (or remaining balance) as 0.
- [PMT] Display “PMT=-8,849.00” Returns the monthly payment to the bank. This result is negative (-). This is because you are pay out the money from your pocket.