r"""
Witt's compound-interest tables
===============================

Richard Witt's *Arithmeticall Questions* (London, 1613) was the first
English book of compound-interest tables. For a given rate it listed,
year by year, the amount of 1, the present value of 1, and the value of
an annuity of 1, so that a clerk could price a loan or a lease with a
look-up and a multiplication. This script prints such a table at 10% and
uses it to price an annuity.
"""

# %%
import matplotlib.pyplot as plt

from financialkit.time_value import annuity_present_value, compound_interest_table

# %%
# A table at 10%
# --------------

table = compound_interest_table(0.10, 10)
print(" year   amount of 1   PV of 1   annuity PV   annuity FV")
for k, a, v, an, sn in zip(table.periods, table.amount, table.discount, table.annuity_present, table.annuity_future, strict=True):
    print(f"{k:5d} {a:13.5f} {v:9.5f} {an:12.5f} {sn:12.5f}")

# %%
# Using the table
# ---------------
# A lease paying 50 a year for 7 years: read a_7 off the table.

print(f"from the table: 50 x {table.annuity_present[6]:.5f} = {50 * table.annuity_present[6]:.2f}")
print(f"direct:         {annuity_present_value(50.0, 0.10, 7):.2f}")

# %%
# The four columns
# ----------------

fig, axes = plt.subplots(1, 2, figsize=(11, 4))
axes[0].plot(table.periods, table.amount, "o-", label="amount of 1, (1+i)^n")
axes[0].plot(table.periods, table.discount, "s-", label="present value of 1, v^n")
axes[0].set_xlabel("years")
axes[0].legend()
axes[1].plot(table.periods, table.annuity_present, "o-", label="annuity present value")
axes[1].plot(table.periods, table.annuity_future, "s-", label="annuity accumulated value")
axes[1].set_xlabel("years")
axes[1].legend()
fig.suptitle("Compound-interest table at 10%")
fig.tight_layout()

plt.show()