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#![allow(unused_imports)] //! **Future value _annuity_ calculations**. Given a series of cashflows, a number of periods such as years, and a fixed //! interest rate, what is the value of the series of cashflows (annuity) at the final payment? //! //! For most common usages, we recommend the [`future_value_annuity_solution`](./fn.future_value_annuity_solution.html) function, which provides a better debugging experience and additional features. //! //! ## Example //! ``` //! let (rate, periods, annuity, due) = (0.034, 10, 500, false); //! let fv_ann = finance_solution::future_value_annuity_solution(rate, periods, annuity, due); //! dbg!(fv_ann); //! ``` //! Outputs to terminal: //! ```text //! { //! calculated_field: FutureValueAnnuity, //! rate: 0.034, //! periods: 10, //! present_value: -4179.341028819186, //! future_value: -5838.660162934523, //! due_at_beginning: false, //! payment: 500.0, //! sum_of_payments: 5000.0, //! sum_of_interest: -5018.0011917537095, //! formula: "-500 * ((1. - (1. / (1. + 0.034)).powf(10)) / 0.034);", //! symbolic_formula: "-annuity * ((1. - (1. / (1. + rate)).powf(periods)) / rate);", //! } //! ``` //! // to-do: add "use log::warn;" and helper logs // Needed for the Rustdoc comments and module. use crate::future_value::future_value; use crate::present_value::present_value; use crate::cashflow::*; use crate::assert_approx_equal; fn check_future_value_annuity_parameters(rate:f64, periods:u32, cashflow:f64) { assert!(rate > -1.0); assert!(rate.is_finite()); assert!(cashflow.is_finite()); assert!(periods > 0); } /// Returns the future value of annuity (a series of constant cashflows) at a constant rate. Returns f64. /// /// The future value annuity formula is: /// /// future value ann = sum( cashflow * (1 + rate)<sup>period</sup> ) /// /// or /// /// future value ann = Constant_Cashflow * ((1+periodic_rate)^n -1) / periodic_rate /// /// # Arguments /// * `rate` - The rate at which the investment grows or shrinks per period, /// expressed as a floating point number. For instance 0.05 would mean 5%. Often appears as /// `r` or `i` in formulas. /// * `periods` - The number of periods such as quarters or years. Often appears as `n` or `t`. /// * `cashflow` - The value of the constant cashflow (aka payment). /// * `due_at_beginning` - True if the payment is due at the beginning of the period. Typically the /// payment will be due at the end of the period so this will be false. /// /// # Panics /// The call will fail if `rate` is less than -1.0 as this would mean the investment is /// losing more than its full value every period. /// /// # Examples /// Quick Glance, how to use: /// ``` /// use finance_solution::*; /// let (rate, periods, payment, due_at_beginning) = (0.034, 5, 500, false); /// let my_annuity = future_value_annuity(rate, periods, payment, due_at_beginning); /// assert_approx_equal!(my_annuity, -2_675.8789282); /// ``` /// /// Or use the solution struct (recommended, more helpful to debugging and for student-learning) /// ``` /// use finance_solution::*; /// let (rate, periods, pmt, due_at_beginning) = (0.034, 5, 500, false); /// let my_annuity = future_value_annuity_solution(rate, periods, pmt, due_at_beginning); /// dbg!(&my_annuity); /// ``` /// Outputs to terminal: /// ```text /// { /// calculated_field: FutureValueAnnuity, /// rate: 0.034, /// periods: 5, /// present_value: 2263.9340209510633, /// future_value: 2675.8789281680038, /// due_at_beginning: false, /// payment: 500.0, /// sum_of_payments: 2500.0, /// sum_of_interest: 7439.812949119067, /// formula: "500 * ((1. - (1. / (1. + 0.034)).powf(5)) / 0.034);", /// formula_symbolic: "annuity * ((1. - (1. / (1. + rate)).powf(periods)) / rate);", /// } /// ``` /// ``` /// # use finance_solution::*; /// # let (rate, periods, pmt, due_at_beginning) = (0.034, 5, 500, false); /// # let my_annuity = future_value_annuity_solution(rate, periods, pmt, due_at_beginning); /// // call the value as a method to get the solution value /// let final_answer = my_annuity.future_value(); /// ``` /// /// Another example: Future value of a series of $2000 cashflows. /// ``` /// # use finance_solution::*; /// // The rate is 2.1% per month. /// let rate = 0.021; /// /// // The investment will grow for 12 months. /// let periods = 12; /// /// // The cashflow will be $2,000. /// let cashflow = 2_000; /// /// let due_at_beginning = false; /// /// // Find the future value. /// let future_value_ann = future_value_annuity(rate, periods, cashflow, due_at_beginning); /// dbg!(&future_value_ann); /// /// // Confirm that the future value is correct to four decimal places (one hundredth of a cent). /// // assert_approx_equal!( , future_value_ann); /// ``` pub fn future_value_annuity<T>(rate: f64, periods: u32, annuity: T, due_at_beginning: bool) -> f64 where T: Into<f64> + Copy { let pmt = annuity.into(); check_future_value_annuity_parameters(rate, periods, pmt); // let mut fv_accumulator = 0_f64; // for i in 0..periods { // let future_value = future_value(rate, i as u32, pmt); // fv_accumulator = fv_accumulator + future_value; // } // fv_accumulator // FV_ann = Constant_Cashflow * [ ( (1+periodic_rate)^n -1 )/ periodic_rate ] // let fv_ann= if due_at_beginning { // let mut fv_accumulator = (1. + rate) * pmt; // for i in 0..periods { // let future_value = future_value(rate, i as u32, pmt); // fv_accumulator = fv_accumulator + future_value; // } // fv_accumulator // } else { // pmt * ((1. + rate).powf(periods as f64) - 1.) / rate // }; // fv_ann let fv_ann = -(1. + (rate * due_at_beginning as u32 as f64)) * pmt * ((1. + rate).powf(periods as f64) - 1.) / rate; fv_ann } /// Returns the future value of annuity (a series of constant cashflows) at a constant rate. Returns custom solution struct with additional information and functionality. /// /// Related functions: /// * To calculate a future value returning an f64, use [`present_value_annuity`]. /// * To calculate a future value with a varying rate or varying cashflow or both, use [`present_value_annuity_schedule`]. /// /// The future value annuity formula is: /// /// future value ann = sum( cashflow * (1 + rate)<sup>period</sup> ) /// or /// future value ann = Constant_Cashflow * ((1+periodic_rate)^n -1) / periodic_rate /// /// # Arguments /// * `rate` - The rate at which the investment grows or shrinks per period, /// expressed as a floating point number. For instance 0.05 would mean 5%. Often appears as /// `r` or `i` in formulas. /// * `periods` - The number of periods such as quarters or years. Often appears as `n` or `t`. /// * `cashflow` - The value of the constant cashflow (aka payment). /// * `due_at_beginning` - True if the payment is due at the beginning of the period. Typically the /// payment will be due at the end of the period so this will be false. /// // / # Panics // / The call will fail if `rate` is less than -1.0 as this would mean the investment is // / losing more than its full value every period. // / /// # Examples /// Future value of a $500 annuity (a series of $500 cashflows) at 3.4% for 10 years. /// ``` /// use finance_solution::*; /// let (rate, periods, cashflow, due_at_beginning) = (0.034, 10, 500, false); /// let my_annuity = future_value_annuity_solution(rate, periods, cashflow, due_at_beginning); /// dbg!(&my_annuity); /// ``` pub fn future_value_annuity_solution<T>(rate: f64, periods: u32, cashflow: T, due_at_beginning: bool) -> CashflowSolution where T: Into<f64> + Copy { let annuity = cashflow.into(); let fv = future_value_annuity(rate, periods, annuity, due_at_beginning); let fvann_type= if due_at_beginning { CashflowVariable::FutureValueAnnuityDue } else { CashflowVariable::FutureValueAnnuity }; // check_future_value__annuity_varying_parameters(rate, periods, cashflow); // add due to formulas let formula = format!("-{} * ((1. - (1. / (1. + {})).powf({})) / {});", annuity, rate, periods, rate); let formula_symbolic = format!("-annuity * ((1. - (1. / (1. + rate)).powf(periods)) / rate);"); // let fv = future_value_annuity(rate, periods, cashflow); let pv = present_value(rate, periods, fv, false); CashflowSolution::new(fvann_type, rate, periods, pv, fv, due_at_beginning, annuity, &formula, &formula_symbolic) } #[cfg(test)] mod tests { use super::*; use crate::*; #[test] fn test_future_value_annuity() { let rate = 0.034; let periods = 10; let annuity = 500; let fv = future_value_annuity(rate, periods, annuity, false); // assert_approx_equal!(5838.66016, fv); assert_eq!(-5838.66016, (fv * 100000.).round() / 100000.); } #[test] fn test_future_value_annuity_1() { let rate = 0.034; let periods = 1; let annuity = 500; let fv = future_value_annuity(rate, periods, annuity, false); // assert_approx_equal!(5838.66016, fv); assert_eq!(-500.0000, (fv * 100000.).round() / 100000.); } #[test] fn test_future_value_annuity_2() { let rate = 0.034; let periods = 400; let annuity = 500; let fv = future_value_annuity(rate, periods, annuity, false); // assert_approx_equal!(9455966284.4844600, fv); assert_eq!(-9455966284.4844600, (fv * 100000.).round() / 100000.); } #[test] fn test_future_value_annuity_3() { // big rate let rate = 0.989; let periods = 8; let annuity = 120_000; let fv = future_value_annuity(rate, periods, annuity, false); assert_eq!(-29_599_651.75013, (fv * 100000.).round() / 100000.); } #[test] fn test_future_value_annuity_4() { let rate = 0.00009; let periods = 780; let annuity = 120_000; let fv = future_value_annuity(rate, periods, annuity, false); assert_eq!(-96_959_087.75951, (fv * 100000.).round() / 100000.); } #[test] fn test_future_value_annuity_5() { // negative rate let rate = -0.0314; let periods = 10; let annuity = 13_000; let fv = future_value_annuity(rate, periods, annuity, false); assert_eq!(-113_087.68194, (fv * 100000.).round() / 100000.); } #[test] fn test_future_value_annuity_6() { // big negative rate let rate = -0.999; let periods = 10; let annuity = 13_000; let fv = future_value_annuity(rate, periods, annuity, false); assert_eq!(-13_013.01301, (fv * 100000.).round() / 100000.); } #[test] fn test_future_value_annuity_7() { // big negative rate, big periods // note: the convergence with the previous test let rate = -0.999; let periods = 780; let annuity = 13_000; let fv = future_value_annuity(rate, periods, annuity, false); assert_eq!(-13_013.01301, (fv * 100000.).round() / 100000.); } }