{ "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: {target_variable_lhs} = {formula_symbolic_rhs}", "substitute_values": "Now, we substitute the known values: {target_variable_lhs} = {formula_with_values_rhs}", "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}.", "identify_gradient_parameters": "Identify the parameters of the arithmetic gradient series:", "state_formula_annuity_component": "The formula for the present worth of the base annuity component (P_A) is: P_A = A1 * (P/A, i, N) which is A1 * [((1 + i)^N - 1) / (i * (1 + i)^N)]", "calculate_pv_annuity_component": "Calculating the present worth of the base annuity component (P_A):", "state_formula_gradient_component": "The formula for the present worth of the arithmetic gradient component (P_G) is: P_G = G * (P/G, i, N) which is G * [(((1 + i)^N - (i * N) - 1) / (i^2 * (1 + i)^N))]", "calculate_pv_gradient_component": "Calculating the present worth of the arithmetic gradient component (P_G):", "state_formula_total_pv": "The total present worth (P_total) is the sum of the present worth of the annuity and gradient components: P_total = P_A + P_G", "sum_pv_components": "Summing the present worth components:" }, "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", "A1_base_annuity": "base annuity amount", "G_gradient_amount": "arithmetic gradient amount", "N_periods": "number of periods", "P_A_component": "present worth of the annuity component", "P_G_component": "present worth of the gradient component", "P_gradient_series": "total present worth of the arithmetic gradient series", "I_simple": "simple interest amount", "F_simple": "future value with simple interest", "F_compound": "future value with compound interest", "t_years": "time period in years (for compounding)", "i_simple_equivalent": "equivalent simple interest rate", "F_maturity": "maturity value (for Banker's Discount)", "P_proceeds": "proceeds from discounted loan", "Db_discount_amount": "banker's discount amount", "F_continuous": "future value with continuous compounding" }, "compounding_frequency_adverbs": { "annually": "annually", "semi-annually": "semi-annually", "quarterly": "quarterly", "monthly": "monthly", "bi-monthly": "bi-monthly", "semi-monthly": "semi-monthly", "continuously": "continuously" } }