You can quickly perform compounding interest calculations using the Time & Value of Money (TVM) keys. In TVM calculations, the payment amount is considered constant over the payment period.

The TVM keys access special variables, or registers, as follows:

**n**- Number of payments.**i**- Interest expressed as a percentage.**PV**- Present or initial value.**PMT**- Payment amount.**FV**- Future or final value.

Given a series of four known values in any order, you can calculate the remaining unknown in a single key press. The calculator will automatically determine whether your key press is being used to input a value, or whether you require a result.

You can see the contents of the TVM registers at any time from the memory page in the Paper Roll Window. You may even change the values from here. Note, that unlike other memory registers, TVM values are not stored when the application closes.

The following examples are given using Reverse Polish Notation. If you are using the prefix algebraic, note that the TVM register functions are postfix.

When calculating the number of payments, some financial calculators round down the result to the nearest integer, thus giving the number of full payments. DreamCalc does not round down; instead it returns the number of full payments plus the fractional component of the final payment.

Payments can be made either at the beginning of a payment period (payments in advance or annuities due) or at
the end of the period (payments in arrears or ordinary annuities). Use the **[BEG/END]** button to toggle
between the BEGIN (in advance) setting and END (in arrears) setting. This affects the results of your
calculations because in BEGIN mode, interest will be accrued over longer periods than in END mode.

**Example:** *Suppose that you have $2,000 today and can invest this amount at 12% APR over the next 5
years with quarterly compounding interest. Determine the value of the investment after 5 years.*

Put the calculator into the END payment mode. In other words, payments are to be made at the end of each period .

In RPN mode, key in the following:

-2000 [PV](stores -2000 in the PV register)5 [ENTER] 4 [×] [n](stores 20, i.e. 5 years of quarterly periods in the n register)12 [ENTER] 4 [÷] [i](stores 3, i.e. the quarterly interest rate in the i register)0 [PMT](no other payments)[FV]Displays: 3612.22

Notes. We enter a negative value into PV because we are investing (or paying out) this value. See the sign convention for more information. Our quarterly interest rate value assumes US rate rules.

**Example:** *You will receive $150 per month for the next five years. If you invest these payments at
an annual rate of 8%, what are your accumulated funds at the end of the five years?*

Put the calculator into the BEGIN payment mode. In other words, payments are to be made at the start of each period.

Key in the following:

[BEG/END](set BEGIN mode if required)5 [12×](stores 60 month periods in n registers)0 [PV](nothing today)150 [PMT](you receive payments of 150 each period)8 [12÷](monthly interest stored in i register)[FV]Displays: -11095.00

In the following examples, we use European and Canadian effective annual rates. Ensure that the calculator is in the END payment mode for these examples.

**Example:** *You take out a loan for 5000 GBP to be repaid over 3 years (or 36 months). Given a 12%
APR, what is the monthly repayment amount?*

In this calculation, ensure the calculator is set to use the **monthly rule** for effective annual rate
calculations.

12 [EMR](calculates monthly rate)Displays: 0.95[i](enters 0.95 value into i register)36 [n](enters 36 periods into n register)5000 [PV](enters 5000 received into Present Value)0 [FV](enters zero as future value, i.e. loan repaid)[PMT](calculates payment amount)Displays: -164.61(we pay out 164.61 GBP each month)

**Example:** *You take out a loan for 9000 $CAN to be repaid at $250 per month, at 13.5% APR. How long
will the loan take to repay?*

In this calculation, ensure that the calculator is set to use the **Canadian rule** for effective annual
rate calculations.

13.5 [EMR](calculates monthly rate)Displays: 1.09[i](enters 1.09 value into i register)9000 [PV](enters 9000 received into Present Value)-250 [PMT](we pay out $250 each period)0 [FV](enters zero as future value, i.e. loan repaid)[n](calculates the number of payments)Displays: 46.02(46 months + one partial payment for 0.02*250)

See also: Discounted Cashflow Calculations