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@rick7661
Created June 13, 2021 11:49
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Calculates total investment return by fixed investment per term, fixed interest per term and number of terms. It is used only to project expected return for a fixed amount, fixed term investment with fixed interest.
import Foundation
// MARK: - Usage: Paste the source code in Xcode Playground and run the examples
// MARK: - Parameters
let fortnightlyInvest: Decimal = 800
let monthlyInvest: Decimal = fortnightlyInvest / 14 * 365 / 12
let yearlyInvest: Decimal = fortnightlyInvest / 14 * 365
let interest: Decimal = 0.08
let years: Int = 10
// MARK: - Functions
/// Total investment return as a formula:
/// `f(p, i, n) = p * (1 + i)^n + f(p, i, n - 1)`
/// - Parameters:
/// - p: Investment per term. E.g. $100 per year, enter 100.
/// - i: Interest per term. E.g. An yearly interst of 10% should be 0.1.
/// - n: Number of terms. E.g. 10 years, enter 10.
/// - Returns: Total return at the end of investment.
func totalReturn_recursion(investmentPerTerm p: Decimal,
interestPerTerm i: Decimal,
numberOfTerms n: Int) -> Decimal {
guard n > 1 else {
return p * (1 + i)
}
return p * pow((1 + i), n) + totalReturn_recursion(investmentPerTerm: p,
interestPerTerm: i,
numberOfTerms: n - 1)
}
/// Total investment return as a formula:
/// `f(p, i, n) = p * [(1 + i)^n + (1 + i)^(n - 1) + ... + (1 + i)^1]`
/// `= p * [(1 + i)^1 + (1 + i)^2 + ... + (1 + i)^n]`
/// - Parameters:
/// - p: Investment per term. E.g. $100 per year, enter 100.
/// - i: Interest per term. E.g. An yearly interst of 10% should be 0.1.
/// - n: Number of terms. E.g. 10 years, enter 10.
/// - Returns: Total return at the end of investment.
func totalReturn_loop(investmentPerTerm p: Decimal,
interestPerTerm i: Decimal,
numberOfTerms n: Int) -> Decimal {
var accumulator: Decimal = 0
for terms: Int in 1 ... n {
accumulator += pow((1 + i), terms)
}
return p * accumulator
}
/// Total investment return as a formula:
/// `f(p, i, n) = p * (1 + i) * ((1 + i)^n - 1) / i`
/// - Parameters:
/// - p: Investment per term. E.g. $100 per year, enter 100.
/// - i: Interest per term. E.g. An yearly interst of 10% should be 0.1.
/// - n: Number of terms. E.g. 10 years, enter 10.
/// - Returns: Total return at the end of investment.
func totalReturn_formula(investmentPerTerm p: Decimal,
interestPerTerm i: Decimal,
numberOfTerms n: Int) -> Decimal {
return p * (1 + i) * (pow((1 + i), n) - 1) / i
}
// MARK: - Examples
// Invest yearly, with fixed yearly interest, for a fix number of years. Recursion.
print(totalReturn_recursion(investmentPerTerm: yearlyInvest,
interestPerTerm: interest,
numberOfTerms: years))
// Invest yearly, with fixed yearly interest, for a fix number of years. Loop.
print(totalReturn_loop(investmentPerTerm: yearlyInvest,
interestPerTerm: interest,
numberOfTerms: years))
// Invest yearly, with fixed yearly interest, for a fix number of years. Formula.
print(totalReturn_formula(investmentPerTerm: yearlyInvest,
interestPerTerm: interest,
numberOfTerms: years))
// Invest monthly, with fixed monthly interest, for a fix number of months. Formula.
print(totalReturn_formula(investmentPerTerm: monthlyInvest,
interestPerTerm: interest / 12,
numberOfTerms: years * 12))
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