# TVM - Time Value of Money¶

Author

Ken Kundert

Version

0.3.1

Released

2019-04-08

## What?¶

Time value of money calculations relate the following quantities:

• future value

• present value

• payments

• number of periods

• discount rate

tvm computes one of these values (other than discount rate) given the others.

The number of periods is split between two values, the number of years and the number of periods per year (the frequency).

## Getting Started¶

Install using:

```pip3 install --user tvm
```

This installs tvm to ~/.local/bin; make sure this directory is on your path.

Usage:

```tvm [options] [fv|pv|pmt|years]
```

Options:

```-f <val>, --fv <val>     future value
-p <val>, --pv <val>     present value
-P <val>, --pmt <val>    payment per period
-y <val>, --years <val>  total number of years
-n <val>, --freq <val>   number of payments per year
-r <val>, --rate <val>   annual discount rate
-i, --ignore             ignore any previously specified values
```

If a value is not given it is recalled from the previous invocation. Specify –ignore to use the default values for all unspecified options, which are: pv=0, fv=0, pmt=0, years=30, freq=12.

When the program runs, it always prints the computed value first, and then prints the remaining values to make it easy for you to confirm that you used the right values.

## Savings Accounts¶

Consider case where you have a interest bearing account that pays 5% per annum compounded monthly. If you start with \$10,000, you can compute the amount you will have after 5 years with:

```tvm --pv=10000 --rate=5 --freq=12 --years=5 fv
```

The amount in 5 years is referred to as the future value (fv). The current amount is the present value (pv). The frequency is the number of periods per year. The program responds with:

```fv = \$12,833.59
pv = \$10,000.00
pmt = \$0.00
r = 5%
N = 60
```

N is the total number of periods and equals the product of the years and the number of periods per year.

You can specify values with SI scale factors, units, and commas. The units and commas are ignored. So you can do the same thing with either:

```tvm --pv='\$10,000' --rate=5% --freq=12 --years=5 fv
```

or:

```tvm --pv=10k --rate=5% --freq=12 --years=5 fv
```

The quotes are needed in the first case to prevent \$ from being interpreted by the shell.

tvm remembers the values specified on the previous invocation and uses them if they are not specified. This allows you to rapidly run what-if experiments without having to re-specify values that do not change. So, once you have run the first command, you can now quickly determine how much you will have in 10 years using:

```tvm -y 10

fv = \$16,470.09
pv = \$10,000.00
pmt = \$0.00
r = 5%
N = 120
```

Without changing anything else, you can determine what happens if you make an additional \$100 contribution each month:

```tvm --pmt 100

fv = \$31,998.32
pv = \$10,000.00
pmt = \$100.00
r = 5%
N = 120
```

## Loans¶

You can also use tvm to explore loans. For example, you can compute the payment for a mortgage given the principal, interest rate, and length:

```tvm --ignore --pv=-250k --rate=4.375 --years=30 pmt

pmt = \$1,248.21
pv = -\$250,000.00
fv = \$0.00
r = 4.38%
N = 360
```

The –ignore option was added so that we start from scratch; any values that were previously specified are ignored.

You can now understand how paying a little extra affects how long it takes to pay off the loan using:

```tvm --pmt=1.5k years

years = 21.42
pv = -\$250,000.00
pmt = \$1,500.00
fv = \$0.00
r = 4.38%
N = 257.08
```

To compute the payments for a 5-year interest only balloon mortgage, use:

```tvm -y 5 -f -250k pmt

pmt = \$911.46
pv = -\$250,000.00
fv = -\$250,000.00
r = 4.38%
N = 60
```