The time value of money¶

Money is a thing which can’t exist without human beings. Before new money is made, someone somewhere has to generate its value.

In modern Western banking, that value derives from a promise to pay. In other words, a debt of one sort or another.

In Tallywallet, debts are recorded with a promissory Note. Your Python script begins like this:

import datetime
from decimal import Decimal

from tallywallet.common.finance import Note

Below I’ll show how to use Tallywallet to work out the value of debt over time. The examples are taken from Schaum’s Mathematics of Finance, 2nd edition.

Lending¶

We’ll start off by recording the details of a historic loan. Back in May of 1995, we lent out $1500 at an annualized interest rate of 8%. The loan was due to be repaid 90 days later:

note = Note(
    date=datetime.date(1995, 5, 11),
    principal=1500,
    currency="$",
    term=datetime.timedelta(days=90),
    interest=Decimal("0.08"),
    period=datetime.timedelta(days=360)
)

What was the simple value of this promise on maturity?:

from tallywallet.common.finance import value_simple

print(value_simple(note))

If you run this Python script now, you’ll see that it came to $1530.00.

The value_simple function applies when there’s one interest period for the term of the note. When the debt spans multiple interest periods, you’d calculate the value of the note with value_series.

We’ll see the flexibility of this function in a moment. For now, let’s fill out its parameters with the attributes of the promissory note to confirm our previous answer:

from tallywallet.common.finance import value_series

print(list(value_series(**vars(note))))

This gives us an output of [(datetime.date(1995, 8, 9), Decimal('1530.0000'))].

Discounting¶

As we recall, in the Spring of 1995 we found ourselves short of cash. We couldn’t wait for our loan to be paid, so in July we sold on the debt to a business contact. He agreed to discount the loan at 9%.

valueAtMaturity = value_simple(note)
dateOfSale = datetime.date(1995, 7, 2)
termRemaining = note.date + note.term - dateOfSale
discount = Decimal("0.09")

We can use value_series to work out how much the debt is worth as cash. We start from the date of maturity, and work back in time, supplying the discounted interest rate:

deal = list(value_series(
    date=note.date + note.term,
    principal=valueAtMaturity,
    term=(-termRemaining),
    period=note.period,
    interest=discount)
)

When we print out the result of the deal we get:

[(datetime.date(1995, 7, 2), Decimal('1515.466'))]

Amortization¶

Now let’s try something a little closer to home.

A mortgage is what happens when interest is allowed to compound against a loan. The creditor demands regular payments, but to begin with they mostly go to supply interest on the debt; they hardly pay off the principal at all. Slowly, according to a process of amortization, the surplus to interest reduces what’s owing.

Tallywallet can construct a complete amortization schedule for this kind of debt.

Here’s an example. A debt of $6000 with interest at 16% compounded twice every year is to be amortized by equal semiannual payments over the next 3 years, the first payment due in 6 months.

from tallywallet.common.finance import schedule

now = datetime.datetime.utcnow()
loan = Note(
    date=now,
    principal=6000,
    currency="$",
    term=datetime.timedelta(days=360*3),
    interest=Decimal("0.16"),
    period=datetime.timedelta(days=180)
)

plan = list(schedule(loan, places=0))

You’ll find plan to be a sequence of objects, each specifying the amount and date of payment, along with how that’s to be shared between interest and debt. The remaining balance is also calculated:

[
    Amortization(
        date=datetime.datetime(2015, 2, 17, 16, 5, 20, 0),
        payment=Decimal('1298'),
        interest=Decimal('480.000'),
        repaid=Decimal('818.000'),
        balance=Decimal('5182.000')
    ),
    Amortization(
        date=datetime.datetime(2015, 8, 16, 16, 5, 20, 0),
        payment=Decimal('1298'),
        interest=Decimal('414.560000'),
        repaid=Decimal('883.440000'),
        balance=Decimal('4298.560000')
    ),
    Amortization(
        date=datetime.datetime(2016, 2, 12, 16, 5, 20, 0),
        payment=Decimal('1298'),
        interest=Decimal('343.884800000'),
        repaid=Decimal('954.115200000'),
        balance=Decimal('3344.444800000')
    ),
    Amortization(
        date=datetime.datetime(2016, 8, 10, 16, 5, 20, 0),
        payment=Decimal('1298'),
        interest=Decimal('267.555584000000'),
        repaid=Decimal('1030.444416000000'),
        balance=Decimal('2314.000384000000')
    ),
    Amortization(
        date=datetime.datetime(2017, 2, 6, 16, 5, 20, 0),
        payment=Decimal('1298'),
        interest=Decimal('185.120030720000000'),
        repaid=Decimal('1112.879969280000000'),
        balance=Decimal('1201.120414720000000')
    ),
    Amortization(
        date=datetime.datetime(2017, 8, 5, 16, 5, 20, 0),
        payment=Decimal('1297.210047897600000000'),
        interest=Decimal('96.089633177600000000'),
        repaid=Decimal('1201.120414720000000000'),
        balance=Decimal('0')
    )
]