Financial Planning with Python: Six Key Coefficients for Financial Planning

The calculation methods are just examples.

Future Value Factor

A coefficient to determine the amount after a certain period when the current amount is invested at compound interest.

def shuka(nenri: float, year: int) -> float:
    money = 1
    for _ in range(year):
        money *= 1 + nenri / 100
    return money

for i in range(1, 6):
    print(f"期間5年、年利{i}%の終価係数は{shuka(i, 5):.4f}")

For a 5-year period and 1% annual interest, the future value factor is 1.0510
For a 5-year period and 2% annual interest, the future value factor is 1.1041
For a 5-year period and 3% annual interest, the future value factor is 1.1593
For a 5-year period and 4% annual interest, the future value factor is 1.2167
For a 5-year period and 5% annual interest, the future value factor is 1.2763

Present Value Factor

A coefficient to determine the principal required to reach a certain amount after a certain period.

def genka(nenri: float, year: int) -> float:
    money = 1
    for _ in range(year):
        money /= 1 + nenri / 100
    return money

for i in range(1, 6):
    print(f"期間5年、年利{i}%の現価係数は{genka(i, 5):.4f}")

For a 5-year period and 1% annual interest, the present value factor is 0.9515
For a 5-year period and 2% annual interest, the present value factor is 0.9057
For a 5-year period and 3% annual interest, the present value factor is 0.8626
For a 5-year period and 4% annual interest, the present value factor is 0.8219
For a 5-year period and 5% annual interest, the present value factor is 0.7835

Future Value of an Annuity Factor

A coefficient to determine the total principal and interest after a certain period when a fixed amount is saved every year.

def shuka(nenri: float, year: int) -> float:
    money = 1
    for _ in range(year):
        money *= 1 + nenri / 100
    return money

def nenkin_shuka(nenri: float, year: int) -> float:
    money = 0
    for y in range(year):
        money += shuka(nenri, y)
    return money

for i in range(1, 6):
    print(f"期間5年、年利{i}%の年金終価係数は{nenkin_shuka(i, 5):.4f}")

For a 5-year period and 1% annual interest, the future value of an annuity factor is 5.1010
For a 5-year period and 2% annual interest, the future value of an annuity factor is 5.2040
For a 5-year period and 3% annual interest, the future value of an annuity factor is 5.3091
For a 5-year period and 4% annual interest, the future value of an annuity factor is 5.4163
For a 5-year period and 5% annual interest, the future value of an annuity factor is 5.5256

Sinking Fund Factor

A coefficient to calculate the annual savings amount required to prepare a certain amount of money after a certain period.

def shuka(nenri: float, year: int) -> float:
    money = 1
    for _ in range(year):
        money *= 1 + nenri / 100
    return money

def nenkin_shuka(nenri: float, year: int) -> float:
    money = 0
    for y in range(year):
        money += shuka(nenri, y)
    return money

def gensai_kikin(nenri: float, year: int) -> float:
    return 1 / nenkin_shuka(nenri, year)

for i in range(1, 6):
    print(f"For a 5-year period and {i}% annual interest, the sinking fund factor is {gensai_kikin(i, 5):.4f}")

For a 5-year period and 1% annual interest, the sinking fund factor is 0.1960
For a 5-year period and 2% annual interest, the sinking fund factor is 0.1922
For a 5-year period and 3% annual interest, the sinking fund factor is 0.1884
For a 5-year period and 4% annual interest, the sinking fund factor is 0.1846
For a 5-year period and 5% annual interest, the sinking fund factor is 0.1810

Capital Recovery Factor

A coefficient to calculate the annual withdrawal amount when a fixed current amount is liquidated over a certain period.

def shuka(nenri: float, year: int) -> float:
    money = 1
    for _ in range(year):
        money *= 1 + nenri / 100
    return money

def shihon_kaishu(nenri: float, year: int) -> float:
    ratio = 0
    for y in range(1, year + 1):
        ratio += 1 / shuka(nenri, y)
    return 1 / ratio

for i in range(1, 6):
    print(f"For a 5-year period and {i}% annual interest, the capital recovery factor is {shihon_kaishu(i, 5):.4f}")

For a 5-year period and 1% annual interest, the capital recovery factor is 0.2060
For a 5-year period and 2% annual interest, the capital recovery factor is 0.2122
For a 5-year period and 3% annual interest, the capital recovery factor is 0.2184
For a 5-year period and 4% annual interest, the capital recovery factor is 0.2246
For a 5-year period and 5% annual interest, the capital recovery factor is 0.2310

Present Value of an Annuity Factor

A coefficient to calculate the principal required to receive a fixed amount over a certain period in the future.

def shuka(nenri: float, year: int) -> float:
    money = 1
    for _ in range(year):
        money *= 1 + nenri / 100
    return money

def shihon_kaishu(nenri: float, year: int) -> float:
    ratio = 0
    for y in range(1, year + 1):
        ratio += 1 / shuka(nenri, y)
    return 1 / ratio

def nenkin_genka(nenri: float, year: int) -> float:
    return 1 / shihon_kaishu(nenri, year)

for i in range(1, 6):
    print(f"For a 5-year period and {i}% annual interest, the present value of an annuity factor is {nenkin_genka(i, 5):.4f}")

For a 5-year period and 1% annual interest, the present value of an annuity factor is 4.8534
For a 5-year period and 2% annual interest, the present value of an annuity factor is 4.7135
For a 5-year period and 3% annual interest, the present value of an annuity factor is 4.5797
For a 5-year period and 4% annual interest, the present value of an annuity factor is 4.4518
For a 5-year period and 5% annual interest, the present value of an annuity factor is 4.3295