RPN-38 CX - An HP-38 Simulator for iOS Devices

RPN-38 — TVM Problems

Recognizing a TVM Problem

If a steady stream of constant cash flows occurs between the first and last periods on the cash-flow diagram, the financial problem is a "TVM" (time value of money) problem. The main keys on the RPN-38 that are used to solve a TVM problem are:

n	Number of periods
i	Interest rate per compounding period
PV	Present value (initial cash flow)
PMT	Payment amount
FV	Future value (final cash flow

Any of the above values can be calculated once you key in the other four. The cash-flow diagrams of loans, mortgages, leases, savings accounts, or any contract with regular cash flows of the same amount normally are treated as TVM problems. An example of a cash-flow diagram of a TVM problem would be the following diagram of a 30- year, $75,000.00 mortgage, at 10.5% annual interest, with a $5,000 balloon payment.

One of the values PV, PMT, or FV can be zero in the solution. An example cash-flow 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 HP-38 should be set to End mode, and if it occurs at the beginning of the first period, your HP-38 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 30-year mortgage, what is the maximum purchase price you can afford?

The cash-flow diagram looks like this:

Keys:	Display:	Description:
		Set mode switch to END
30 g 12×	360.00	Stores the length of the mortgage
0 FV	0.00	You will completely payoff the mortgage in 30 years.
11.5 g 12÷	0.96	Interest rate per compounding period (one month).
630 CHS PMT	-630.00	Stores your desired payment as a negative value (money paid out is negative).
PV	63,617.64	Calculates the loan you can afford with a $630 payment.
12000 +	75,617.64	Adds in the $12,000 down payment to give a total purchase price.

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 half-month. The account pays 8.3% annual interest compounded semi-monthly. How much will be in the account on April 15, 2000?

The cash-flow diagram looks like this:

Keys:	Display:	Description:
		Set mode switch to END
2000 CHS PV	-2,000.00	Stores the amount of your initial deposit.
80 CHS PMT	-80.00	Stores the amount of your regular semi-monthly deposits.
8.3 ENTER 24 ÷ i	0.35	Interest rate per compounding period (half a month).
15 ENTER 24 × n	360.00	Stores the number of deposits.
FV	63,963.84	Calculates the balance.

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 cash-flow diagram looks like this:

Keys:	Display:	Description:
		Set mode switch to BEGIN
14 g 12÷	1.17	Stores the desired yield per compounding period.
13500 CHS PV	-13,500.00	Stores the lease price of the car.
7500 FV	7,500.00	Stores the residual (buy-out value).
3 g 12×	36.00	Stores the length of the lease, in months.
PMT	289.19	Calculates the monthly lease payment.

Notice that even if the customer chooses not to buy the car, the lessor still includes a cash-flow 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.