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# HP 12c Financial Calculator - Solving for Lease Payments

## Lease payments

A lease is an agreement for one company or individual to use an asset owned by another company or individual for a
specified time. The payment required (often called the “rent”) during this lease period depends upon the interest rate
involved and the decline in the value of the asset with experience while being used. The projected value of the asset at the end
of the period is often called the residual value. Lease payments are usually made in advance, which requires them to be
treated as annuities due.

For the HP 12c to solve problems involving leases or annuities due, it must be in 'Begin' mode.

This mode is changed using the blue-shifted BEG function, located on the key, or . This function will change
the calculator to view payments happening at the beginning of periods rather than the end. When the HP 12c is in 'Begin'
mode, the word 'BEGIN' will show in the display. To reset the calculator for ordinary annuities, press .

If you receive an unexpected result when solving an annuity problem, make sure that the calculator is in the proper mode
and try resolving the problem.

note:It may also be difficult to determine the actual interest rate involved in a lease. The examples below assume this interest rate is known.

## The HP 12c TVM

Standard HP 12c features solve these types of problems with the five TVM keys , , , and . These
keys are associated to the five TVM registers n, i, PV, PMT and FV. To set any of these registers to a known value,
calculate or key it in and press the corresponding key. Enter each of the four known TVM values, press its related key,
then press the key that represents the unknown, fifth value to calculate it.

There are also two functions meant to be an aid when entering or retrieving annual values for and : and . Pressing is the same as pressing , meaning the number of years can be keyed in
and stored as number of months automatically. Pressing is the same as pressing , meaning the yearly interest rate can be keyed in and stored as monthly interest rate automatically. It is also possible to
retrieve the yearly-related values by pressing (number of years) and/or (yearly interest rate)
whenever necessary.

## Practice solving for the payment on a lease

### Example 1

A company is considering leasing a machine that costs $20,000 today. The lease would be for 5 years with
a residual value of $6,000 for the machine at the end of that period. The agreement calls for the use of an
8%, compounded monthly, interest rate. If monthly lease payments will be made, what is the size of the
lease payment required?

### Solution

To solve this leasing problem, the calculator will need to be in 'Begin' mode. The solution below assumes
the HP 12c calculator is not already in this mode. If the calculator is already in this mode, the keystrokes of shown below may be omitted. Remember to change the calculator back to End mode before
solving ordinary annuities again.

### Answer

The result is $321.72.

### Example 2

An individual is considering leasing a car that costs $26,995 today. The lease would be for 2 years with a
residual value of $14,000 for the vehicle at the end of that period. The agreement calls for the use of a 6%,
compounded monthly, interest rate. If monthly lease payments will be made, what is the size of the lease
payment required?

### Solution

### Answer

The result is $642.73.

### Example 3

A company is considering leasing a machine that costs $24,505 today. The lease would be for 3 years with
a residual value of $11,000 for the machine at the end of that period. The agreement calls for the use of a
10%, compounded monthly, interest rate. If monthly lease payments will be made, what is the size of the
lease payment required?

### Solution

### Answer

The result is $523.08.

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