RPN38 — TVM Problems
Recognizing a TVM Problem
If a steady stream of constant cash flows occurs between the first and last periods on the cashflow diagram, the financial problem is a "TVM" (time value of money) problem. The main keys on the RPN38 that are used to solve a TVM problem are:
One of the values PV, PMT, or FV can be zero in the solution. An example cashflow diagram of a savings account with a single deposit and a single withdrawal five years later is shown below. Interest is compounded monthly. This is an example of a TVM problem where PMT is zero. Before you start a TVM calculation, you should identify whether the first payment (PMT) occurs at the beginning or end of the first period. If the first payment occurs at the end of the first period, your HP38 should be set to End mode, and if it occurs at the beginning of the first period, your HP38 should be set to Begin mode. To change modes, set the mode switch to either BEGIN or END. Mortgages and loans typically require End mode, while leases and savings plans typically require Begin mode. Mortgage payments are typically due at the beginning of the month. However, you usually wait one month before making the first payment so End mode is used. 

A Home Mortgage
After careful consideration of your personal finances, you've decided that the maximum monthly mortgage payment you can afford is $630.00. You can make a $12,000 down payment, and annual interest rates are currently around 11.5%. If you obtain a 30year mortgage, what is the maximum purchase price you can afford?
The cashflow diagram looks like this:


An Individual Retirement Account
You opened an individual retirement account on April 15, 1985, with a deposit of $2,000. Thereafter, you have deposited $80.00 into the account at the end of each halfmonth. The account pays 8.3% annual interest compounded semimonthly. How much will be in the account on April 15, 2000?
The cashflow diagram looks like this:


Calculating a Lease Payment
A customer at your car dealership wishes to lease a new car valued at $13,500 for 3 years. The lease includes an option to buy the car for $7,500 at the end of the the lease. The first monthly payment is due the day the customer drives the car off the lot. What will the payments be to yield your leasing company 14% annually (compounded monthly)? Calculate the payments from your (the lessor's) point of view.
The cashflow diagram looks like this:
Notice that even if the customer chooses not to buy the car, the lessor still includes a cashflow coming in at the end of the lease equal to the residual value of the car. Whether the customer buys the car or it is sold on the open market, the lessor expects to recover at least $7,500. 
