Examples

This section contains practical examples demonstrating how to use qfinbox for various Time Value of Money calculations and financial analysis tasks.

Basic TVM Examples

Present and Future Value Calculations

from qfinbox.tvm import basic

# Calculate present value of $10,000 received in 5 years at 6% annual rate
pv = basic.present_value(fv=10000, rate=0.06, periods=5)
print(f"Present Value: ${pv:.2f}")  # $7,472.58

# Calculate future value of $5,000 invested for 10 years at 8% annual rate
fv = basic.future_value(pv=5000, rate=0.08, periods=10)
print(f"Future Value: ${fv:.2f}")   # $10,794.62

# Find the interest rate for doubling money in 10 years
rate = basic.interest_rate(pv=1000, fv=2000, periods=10)
print(f"Required Rate: {rate:.2%}")  # 7.18%

Annuity Examples

Retirement Planning

from qfinbox.tvm import annuities

# Calculate present value of $2,000 monthly payments for 25 years at 7% annual rate
monthly_rate = 0.07 / 12
periods = 25 * 12
pv = annuities.pv_ordinary_annuity(pmt=2000, rate=monthly_rate, periods=periods)
print(f"Present Value of Retirement Income: ${pv:,.2f}")  # $312,816.55

# Calculate future value of $500 monthly savings for 30 years at 6% annual rate
monthly_rate = 0.06 / 12
periods = 30 * 12
fv = annuities.fv_ordinary_annuity(pmt=500, rate=monthly_rate, periods=periods)
print(f"Future Value of Savings: ${fv:,.2f}")  # $502,258.15

# Calculate perpetuity value for $10,000 annual payments at 5% rate
perpetuity = annuities.perpetuity_value(pmt=10000, rate=0.05)
print(f"Perpetuity Value: ${perpetuity:,.2f}")  # $200,000.00

Bond Valuation Examples

Corporate Bond Analysis

from qfinbox.tvm import bonds

# Price a 10-year corporate bond with 6% coupon, $1000 face value, 5% market rate
price = bonds.bond_price(face_value=1000, coupon_rate=0.06,
                       market_rate=0.05, periods=10)
print(f"Bond Price: ${price:.2f}")  # $1,077.22

# Calculate yield for bond trading at $950 with 5% coupon
bond_yield = bonds.bond_yield(price=950, face_value=1000,
                            coupon_rate=0.05, periods=8)
print(f"Bond Yield: {bond_yield:.2%}")  # 5.74%

# Calculate duration for interest rate risk assessment
duration = bonds.bond_duration(face_value=1000, coupon_rate=0.04,
                             market_rate=0.05, periods=15)
print(f"Modified Duration: {duration:.2f} years")  # 10.38 years

Loan Analysis Examples

Mortgage Calculations

from qfinbox.tvm import loans
import pandas as pd

# Calculate monthly payment for $300,000 mortgage at 4.5% for 30 years
principal = 300000
annual_rate = 0.045
years = 30
monthly_rate = annual_rate / 12
periods = years * 12

payment = loans.loan_payment(principal=principal, rate=monthly_rate, periods=periods)
print(f"Monthly Payment: ${payment:.2f}")  # $1,520.06

# Calculate remaining balance after 10 years
payments_made = 10 * 12
balance = loans.loan_balance(principal=principal, rate=monthly_rate,
                           periods=periods, payments_made=payments_made)
print(f"Remaining Balance: ${balance:,.2f}")  # $234,896.47

# Generate amortization schedule (first 12 months)
schedule = loans.amortization_schedule(principal=principal, rate=monthly_rate,
                                     periods=periods, num_payments=12)
df = pd.DataFrame(schedule)
print(df.head())

Cash Flow Analysis Examples

Investment Project Evaluation

from qfinbox.tvm import cashflow

# Evaluate investment project with initial cost and 5-year cash flows
cash_flows = [-100000, 25000, 30000, 35000, 40000, 45000]
discount_rate = 0.12

# Calculate Net Present Value
project_npv = cashflow.npv(rate=discount_rate, cash_flows=cash_flows)
print(f"Project NPV: ${project_npv:,.2f}")  # $16,747.82

# Calculate Internal Rate of Return
project_irr = cashflow.irr(cash_flows=cash_flows)
print(f"Project IRR: {project_irr:.2%}")  # 19.54%

# Calculate Payback Period
payback = cashflow.payback_period(cash_flows=cash_flows)
print(f"Payback Period: {payback:.2f} years")  # 3.44 years

# Calculate Profitability Index
pi = cashflow.profitability_index(rate=discount_rate, cash_flows=cash_flows)
print(f"Profitability Index: {pi:.3f}")  # 1.167

Advanced Examples

Complex Financial Scenarios

from qfinbox.tvm import basic, annuities, cashflow
import numpy as np

# Education funding calculation
# Child is 5 years old, college starts at 18 (13 years from now)
# College costs $50,000/year for 4 years, inflation 3% annually

# Calculate future cost of college
years_to_college = 13
annual_cost_today = 50000
inflation_rate = 0.03

future_costs = []
for year in range(4):  # 4 years of college
    periods = years_to_college + year
    future_cost = basic.future_value(pv=annual_cost_today,
                                   rate=inflation_rate, periods=periods)
    future_costs.append(future_cost)

print("Future College Costs:")
for i, cost in enumerate(future_costs, 1):
    print(f"Year {i}: ${cost:,.2f}")

# Calculate present value of total college costs
investment_rate = 0.07
total_pv = sum(basic.present_value(fv=cost, rate=investment_rate,
                                 periods=years_to_college + i)
              for i, cost in enumerate(future_costs))
print(f"\nPresent Value of College Costs: ${total_pv:,.2f}")

# Calculate required monthly savings
monthly_rate = investment_rate / 12
months = years_to_college * 12
required_savings = total_pv / annuities.fv_ordinary_annuity(pmt=1,
                                                          rate=monthly_rate,
                                                          periods=months)
print(f"Required Monthly Savings: ${required_savings:,.2f}")

Note

All examples use realistic financial scenarios and demonstrate practical applications of the qfinbox TVM functions. The calculations assume standard financial conventions and can be adapted for specific use cases.