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.
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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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