New Firmware for HP Prime and HP15c CE

# How to use Time Value of Money - Loans

The 5 top left keys of your HP12c keyboard, named n, i, PV, PMT and FV are the Time Value of Money keys. It serves, as we will show, to calculate easily loans, repayment schedules, savings for pension, etc.

Let's first agree on conventions.

• "+" is for amounts you have or you receive; "-" is for amounts you pay or you owe.
• n is the number of periods of payment. Typically, n may be years or months. Other periods are possible as we will see.
• i is the interest rate for each period.
• PV is the Present Value, that may be thought as the initial amount in some cases.
• PMT is the periodical payment. Again, "+" if you receive it, "-" if you pay it. In general it will be composed of interest and principal.
• FV is the future value

Now the rules with these keys:

• When you enter a number and press one of the keys, the number gets stored in the variable.
• When you press one of the keys after having pressed another (for example to enter a number), the system tries to solve for that variable based on what is on the other 5 variables.
• For monthly periods: you can enter the number of months based on a number of years by keying g n (which multiplies the number by 12), and you can enter the monthly interest by keying the yearly interest and pressing g i (which divides the interest by 12)
• You can retrieve the contents of any such variable (when you do not want it to be recalculated for some reason) by keying RCL n, i, PV, PMT, FV; and you can make sure that you store a value there by keying STO n, i, PV, PMT, FV. This will be useful later as you'll see.

Let's imagine some cases.

Loan calculation 1: monthly payment, 200.000€ initial amount, 20 years, complete payment, 6% annual interest. In brackets, actual keystrokes.

• n => 20*12 = 240 [ 20 g n]
• i => 6/12 = 0,5% [ 6 g i ]
• PV => 200000 [ 200000 PV]
• FV => 0 [ 0 FV]
• Calculate monthly payment: [ PMT ] => -1432,86 (negative because you have to pay it)

Loan calculation 2: with the above data, how much will it be left to pay at the end of year 10 ?

• n => 10*12 = 120 [ 10 g n]
• Calculate future value with same interest and payment: [ FV ] => -129062,84 of principal. It is negative because you owe it.

Loan calculation 3: how much have we paid of interest and principal in the first 10 years:

• Follow the loan calculation 1 steps to make sure everything is in its place with the original numbers
• [ 120 f AMORT] => -101006,34 (interest paid)
• [ x<>y ] => 70936,86 (capital paid)
• Pressing now [ RCL PV ] shows what is left to pay: 129063,14. The difference with the above number (0,30 over 120 payments) stems from the fact that you are paying cents, and not the full accuracy of the calculation.

Loan calculation 4: calculate payment if at the end of year 10, interest is changed to 4% going forward

• Copy final value as initial value:
• [ RCL FV ] => -129062,84
• [ CHS ] => 129062,84 (change sign so that it looks like a new loan)
• [ STO PV ] => 129062,84
• ​Change interest to 4%
• ​[ 4 g i ] => 0,33 (inside it is full 10 digit precision)
• ​Put the 10 year left as termination date for the loan, and establish full payment (0 future value)
• ​[ 10 g n] => 120
• [ 0 FV ] => 0
• ​Calculate the monthly amount: press [ PMT ] => -1306,70​