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Society of Actuaries. (2023). Exam FM Sample Questions.

Learning Objective 1: Time Value of Money.

question 1

Description

Bruce deposits 100 into a bank account. His account is credited interest
at an annual nominal rate of interest of 4% convertible semiannually.
At the same time, Peter deposits 100 into a separate account. Peter's
account is credited interest at an annual force of interest of δ.
After 7.25 years, the value of each account is the same.
Calculate δ.

Solution

Imports

import numpy_financial as npf
import numpy as np

Code

def solve_question_1():
    # Given data
    bruce = {
        "principal": 100,  # Principal for Bruce
        "annual_interest_rate": 0.04,  # Annual nominal interest rate for Bruce
        "compounding_frequency": 2,  # Compounded semiannually for Bruce
        "time_years": 7.25,  # Time in years
    }

    # Calculate the future value of Bruce's account
    bruce["account"] = npf.fv(
        rate=bruce["annual_interest_rate"] / bruce["compounding_frequency"],
        nper=bruce["compounding_frequency"] * bruce["time_years"],
        pmt=0,
        pv=-bruce["principal"],
    )

    delta = np.log(bruce["account"] / bruce["principal"]) / bruce["time_years"]

    return delta