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# Time Value of Money (TVM) Overview

#### CALC 1 has 6 Calculators for Time Value of Money Calculations with Equal Payments:

With the Time Value of Money I/YR Calculator you enter an annual interest rate and the number of payments and compounding periods per year using a Focused Calculator.

The Time Value of Money Form Calculator has the same functionality of the Time Value of Money I/YR Calculator but it uses a form so you can see all of the values in one view. These calculators also share the same storage variables so you can switch between them without having to re-enter values.

With the two odd periods calculators you enter a periodic interest rate and they calculate odd periods (the number of periods with fractional parts) differently, like a HP 12CP calculator. See Time Value of Money Compound Interest Formulas for details.

The TVM calculators can be used to solve loan, leasing, savings and other TVM calculations involving equal payments at a fixed interval. The equal payments can be equal to 0. For unequal payments, see Cash Flows.

#### The TVM calculators will calculate any of the 5 following values given a value for the other 4 variables:

TVM Variables
Variable Description
N Number of periods.
i/YR, i Interest rate. (annual, I/YR or periodic, i)
PV The present value.
PMT Payment amount. There are N payments.
FV Future Value.

#### The following parameters are not calculated.

TVM Parameters
Variable Description
P/YR Payments per year. (STO P/YR) (Only on i/YR, Form and HP10bii Calculators)
C/YR Compounding periods per year. (STO C/YR) (Only on the i/YR and Form Calculators)
BEG/END Setting to indicate if the payments are at the beginning or end of each period. (shift BEG or END)

## Cash Flow Diagrams and Signs of Numbers

It is helpful to illustrate TVM calculations with cash-flow diagrams. Cash-flow diagrams are time lines divided into equal segments called compounding (or payment) periods. Arrows show the occurrence of cash flows (payments in or out). Money received is a positive number (arrow up) and money paid out is a negative number (arrow down).

The correct sign (positive or negative) for TVM numbers is essential. The calculations will make sense only if you consistently show payments out as negative and payments in (receipts) as positive. Perform a calculation from the point of view of either the lender (investor) or the borrower, but not both! (This is from a HP 17bii manual)

## Cash Flow Diagrams and the TVM Keys The N key stores or calculates the number of payment periods. The PV key stores or calculates the amount of the present value, or the initial cash flow. Positive for money received or negative for money paid out. The PMT key stores or calculates the amount of each periodic payment. Positive for money received or negative for money paid out.

The diagram above shows the PMT cash flows with the payment mode set to END. The payments occur at the end of the payment periods and coincide with the FV cash flow. The diagram above shows the PMT cash flows with the payment mode set to BEG. The payments occur at the beginning of the payment periods and coincide with the PV cash flow. The FV key stores or calculates the amount of the future value, or the final cash flow. Positive for money received or negative for money paid out. If the payment mode is set to END the last payment coincides with the FV.

TVM Examples