{ "actors_person": ["{person_title} {person_first_name} {person_last_name}", "{person_first_name} {person_last_name}", "{person_title} {person_last_name}"], "actors_company": ["{company_prefix} {company_suffix}", "{company_prefix} {company_industry}"], "actions_loan_present_singular": ["borrows", "takes out a loan for", "secures financing for", "needs a loan of", "is seeking a loan of"], "actions_loan_present_plural": ["borrow", "take out a loan for", "secure financing for", "need a loan of", "are seeking a loan of"], "actions_loan_past_singular": ["borrowed", "took out a loan for", "secured financing for", "received a loan of"], "actions_loan_past_plural": ["borrowed", "took out a loan for", "secured financing for", "received a loan of"], "actions_investment_present_singular": ["invests", "deposits", "puts", "plans to invest", "wants to deposit"], "actions_investment_present_plural": ["invest", "deposit", "put", "plan to invest", "want to deposit"], "actions_investment_past_singular": ["invested", "deposited", "put", "made an investment of"], "actions_investment_past_plural": ["invested", "deposited", "put", "made an investment of"], "actions_repayment_present_singular": ["repays", "settles", "amortizes", "makes a payment on"], "actions_repayment_present_plural": ["repay", "settle", "amortize", "make a payment on"], "actions_repayment_past_singular": ["repaid", "settled", "amortized", "made a payment on"], "actions_repayment_past_plural": ["repaid", "settled", "amortized", "made a payment on"], "actions_receive_present_singular": ["receives", "obtains", "gets", "is due to receive"], "actions_receive_present_plural": ["receive", "obtain", "get", "are due to receive"], "actions_receive_past_singular": ["received", "obtained", "got"], "actions_receive_past_plural": ["received", "obtained", "got"], "actions_earn_present_singular": ["earns", "accumulates", "yields"], "actions_earn_present_plural": ["earn", "accumulate", "yield"], "actions_earn_past_singular": ["earned", "accumulated", "yielded"], "actions_earn_past_plural": ["earned", "accumulated", "yielded"], "time_phrases_duration": ["for a period of", "over", "for", "during"], "time_phrases_point": ["at the end of", "after", "in"], "rate_phrases": ["at a rate of", "with an interest of", "at an annual rate of", "earning interest at"], "compounding_phrases": ["compounded {compounding_frequency_adverb}", "with {compounding_frequency_adverb} compounding"], "purpose_phrases_loan": ["for {item_loan}", "to finance {item_loan}", "to purchase {item_loan}"], "purpose_phrases_investment": ["in {item_investment}", "into {item_investment}", "to grow their capital through {item_investment}"], "question_starters_what_is": ["What is the", "Determine the", "Calculate the", "Find the", "What will be the", "What was the"], "question_starters_how_much": ["How much is the", "How much will be the", "How much was the", "How much should be"], "question_starters_how_long": ["How long will it take for", "How many years are needed for", "What is the time period for"], "scenario_introductions": [ "Consider a scenario where {actor}", "{actor} is planning to", "Suppose {actor}", "Imagine {actor} needs to" ], "scenario_connectors": [ "The terms of the agreement state that", "It is known that", "Given that", "Assuming that" ], "scenario_closures_question_prefix": [ "Based on this information,", "Therefore,", "With these conditions," ], "solution_guidance": { "identify_knowns": "First, let's identify the given values (knowns) in the problem:", "state_formula": "The relevant formula for this problem is:", "substitute_values": "Now, we substitute the known values into the formula:", "perform_calculation": "Performing the calculation:", "intermediate_step": "The intermediate result for {step_name} is:", "final_answer_is": "Therefore, the {unknown_variable_description} is:", "convert_time_to_years": "Convert the time period to years: {original_time_value} {original_time_unit} = {converted_time_value_years} years.", "calculate_interest_rate_per_period": "Calculate the interest rate per compounding period (i): i = r / m = {nominal_rate_decimal} / {compounding_periods_per_year} = {interest_rate_per_period_decimal}.", "calculate_total_periods": "Calculate the total number of compounding periods (n): n = t * m = {time_in_years} years * {compounding_periods_per_year} = {total_periods} periods.", "check_leap_year": "{year} is {is_or_is_not} a leap year.", "days_in_period": "The number of days from {start_date} to {end_date} is {number_of_days} days." }, "variable_descriptions": { "P": "principal amount", "F": "future value", "I": "interest amount", "i_simple_annual": "annual simple interest rate", "n_time_years": "time period in years", "n_time_months": "time period in months", "n_time_days": "time period in days", "r_nominal_annual": "nominal annual interest rate", "m_compounding_periods_per_year": "number of compounding periods per year", "i_rate_per_period": "interest rate per compounding period", "n_total_compounding_periods": "total number of compounding periods", "ER": "effective interest rate", "Db": "banker's discount amount", "d_discount_rate": "discount rate", "Proceeds": "proceeds from the loan", "I_exact_simple": "exact simple interest amount", "F_exact_simple": "future value with exact simple interest", "I_ordinary_simple": "ordinary simple interest amount", "F_ordinary_simple": "future value with ordinary simple interest", "start_date": "start date of the period", "end_date": "end date of the period", "time_base_days": "day count basis for the year (time base)", "n_time_years_fractional": "time period as a fraction of a year" }, "solution_guidance": { "identify_knowns": "First, let's identify the given values (knowns) in the problem:", "state_formula": "The relevant formula for this problem is:", "substitute_values": "Now, we substitute the known values into the formula:", "perform_calculation": "Performing the calculation:", "intermediate_step": "The intermediate result for {step_name} is:", "final_answer_is": "Therefore, the {unknown_variable_description} is:", "convert_time_to_years": "Convert the time period to years: {original_time_value} {original_time_unit} = {converted_time_value_years} years.", "calculate_interest_rate_per_period": "Calculate the interest rate per compounding period (i): i = r / m = {nominal_rate_decimal} / {compounding_periods_per_year} = {interest_rate_per_period_decimal}.", "calculate_total_periods": "Calculate the total number of compounding periods (n): n = t * m = {time_in_years} years * {compounding_periods_per_year} = {total_periods} periods.", "check_leap_year": "{year} is {is_or_is_not} a leap year.", "days_in_period": "The number of days from {start_date} to {end_date} is {number_of_days} days.", "determine_time_base_exact": "For exact simple interest, the time base is the actual number of days in the reference year ({year}), which is {days_in_year} days.", "determine_time_base_ordinary": "For ordinary simple interest, the time base is 360 days.", "calculate_n_time_years_fractional": "Calculate the time as a fraction of a year (t_fractional): t_fractional = number of days / time base = {n_time_days} / {time_base_days} = {n_time_years_fractional_value}." }, "compounding_frequency_adverbs": { "annually": "annually", "semi-annually": "semi-annually", "quarterly": "quarterly", "monthly": "monthly", "bi-monthly": "bi-monthly", "semi-monthly": "semi-monthly", "continuously": "continuously" } }