feat: kata/financing-a-purchase (#847)

* docs: kata description

* feat: kata/financing-a-purchase

* refactor: cast one of the operands of this subtraction operation to a "double".

---------

Co-authored-by: ParanoidUser <[email protected]>

Author: github-actions[bot]

kata/6-kyu/financing-a-purchase/README.md

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+# [Financing a purchase](https://www.codewars.com/kata/financing-a-purchase "https://www.codewars.com/kata/59c68ea2aeb2843e18000109")
+
+The description is rather long, but it tries to explain what a financing plan is.
+
+The fixed monthly payment for a fixed rate mortgage is the amount paid by the borrower every month that ensures
+that the loan is paid off in full, with interest at the end of its term.
+
+The monthly payment formula is based on the annuity formula.
+The monthly payment `c` depends upon:
+
+- `rate` - the monthly interest rate is expressed as a decimal, not a percentage.
+  The monthly rate is simply the **given** yearly percentage rate divided by 100 and then by 12.
+
+- `term` - the number of monthly payments, called the loan's `term`.
+- `principal` - the amount borrowed, known as the loan's principal (or `balance`).
+
+First we have to determine `c`.
+
+We have: `c = n /d` with `n = r LICENSE build.gradle.kts docs gradle gradle.properties gradlew gradlew.bat kata settings.gradle.kts balance`
+and `d = 1 - (1 + r)**(-term)` where `**` is the `power` function (you can look at the reference below).
+
+The payment `c` is composed of two parts. The first part pays the interest (let us call it `int`)
+due for the balance of the given month, the second part repays the balance (let us call this part `princ`) hence for the following month we
+get a `new balance = old balance - princ` with `c = int + princ`.
+
+Loans are structured so that the amount of principal returned to the borrower starts out small and increases with each mortgage payment.
+While the mortgage payments in the first years consist primarily of interest payments, the payments in the final years consist primarily of
+principal repayment.
+
+A mortgage's amortization schedule provides a detailed look at precisely what portion of each mortgage payment is dedicated to each
+component.
+
+In an example of a $100,000, 30-year mortgage with a rate of 6 percents the amortization schedule consists of 360 monthly payments.
+The partial amortization schedule below shows with 2 decimal floats
+the balance between principal and interest payments.
+
+| -- | num_payment | c      | princ  | int    | Balance   |
+|----|-------------|--------|--------|--------|-----------|
+| -- | 1           | 599.55 | 99.55  | 500.00 | 99900.45  |
+| -- | ...         | 599.55 | ...    | ...    | ...       |
+| -- | 12          | 599.55 | 105.16 | 494.39 | 98,771.99 |
+| -- | ...         | 599.55 | ...    | ...    | ...       |
+| -- | 360         | 599.55 | 596.57 | 2.98   | 0.00      |
+
+#### Task:
+
+Given parameters
+
+```
+rate: annual rate as percent (don't forgent to divide by 100*12)
+bal: original balance (borrowed amount) 
+term: number of monthly payments
+num_payment: rank of considered month (from 1 to term)
+```
+
+the function `amort` will return a formatted string (for example):
+
+`"num_payment %d c %.0f princ %.0f int %.0f balance %.0f" (with arguments num_payment, c, princ, int, balance`)
+
+***In Common Lisp:***
+return a list with num-payment, c, princ, int, balance each rounded.
+
+#### Examples:
+
+```
+amort(6, 100000, 360, 1) ->
+"num_payment 1 c 600 princ 100 int 500 balance 99900"
+
+amort(6, 100000, 360, 12) ->
+"num_payment 12 c 600 princ 105 int 494 balance 98772"
+
+```
+
+#### Ref
+
+<https://en.wikipedia.org/wiki/Mortgage_calculator>

kata/6-kyu/financing-a-purchase/main/Finance.java

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+interface Finance {
+  static String amort(double rate, double bal, int term, int numPayment) {
+    rate /= 1200;
+    double c = rate * bal / (1 - Math.pow(1 + rate, -term));
+    double principal = (c - bal * rate) * Math.pow(1 + rate, numPayment - 1.);
+    return String.format("num_payment %d c %.0f princ %.0f int %.0f balance %.0f",
+        numPayment,
+        c,
+        principal,
+        c - principal,
+        bal * (1 - (Math.pow(1 + rate, numPayment) - 1) / (Math.pow(1 + rate, term) - 1)));
+  }
+}

kata/6-kyu/financing-a-purchase/test/FinanceTest.java

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+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+import org.junit.jupiter.params.ParameterizedTest;
+import org.junit.jupiter.params.provider.CsvSource;
+
+class FinanceTest {
+  @ParameterizedTest
+  @CsvSource(textBlock = """
+      7.4, 10215, 24, 20, num_payment 20 c 459 princ 445 int 14 balance 1809
+      7.9, 107090, 48, 41, num_payment 41 c 2609 princ 2476 int 133 balance 17794
+      6.8, 105097, 36, 4, num_payment 4 c 3235 princ 2685 int 550 balance 94447
+      3.8, 48603, 24, 10, num_payment 10 c 2106 princ 2009 int 98 balance 28799
+      """)
+  void sample(double rate, int bal, int term, int numPayments, String expected) {
+    assertEquals(expected, Finance.amort(rate, bal, term, numPayments));
+  }
+}

kata/6-kyu/index.md

@@ -139,6 +139,7 @@
 - [Fibonacci Rabbits](fibonacci-rabbits "5559e4e4bbb3925164000125")
 - [Fibonacci, Tribonacci and friends](fibonacci-tribonacci-and-friends "556e0fccc392c527f20000c5")
 - [Figurate Numbers #1 - Pentagonal Number](figurate-numbers-number-1-pentagonal-number "55ab9eee6badbdaf72000075")
+- [Financing a purchase](financing-a-purchase "59c68ea2aeb2843e18000109")
 - [Financing Plan on Planet XY140Z-n](financing-plan-on-planet-xy140z-n "559ce00b70041bc7b600013d")
 - [Find last Fibonacci digit [hardcore version]](find-last-fibonacci-digit-hardcore-version "56b7771481290cc283000f28")
 - [Find Numbers with Same Amount of Divisors](find-numbers-with-same-amount-of-divisors "55f1614853ddee8bd4000014")