buyingACar.js

// A man has a rather old car being worth $2000. He saw a 
// secondhand car being worth $8000. He wants to keep his 
// old car until he can buy the secondhand one.

// He thinks he can save $1000 each month but the prices of 
// his old car and of the new one decrease of 1.5 percent per 
// month. Furthermore the percent of loss increases by a fixed 
// 0.5 percent at the end of every two months.

// Example of percents lost per month:

// If, for example, at the end of first month the percent of 
// loss is 1, end of second month percent of loss is 1.5, end 
// of third month still 1.5, end of 4th month 2 and so on ...

// Can you help him? Our man finds it difficult to make all 
// these calculations.

// How many months will it take him to save up enough money 
// to buy the car he wants, and how much money will he have left over?

// Parameters and return of function:

// parameter (positive int, guaranteed) startPriceOld (Old car price)
// parameter (positive int, guaranteed) startPriceNew (New car price)
// parameter (positive int, guaranteed) savingperMonth 
// parameter (positive float or int, guaranteed) percentLossByMonth

// nbMonths(2000, 8000, 1000, 1.5) should return [6, 766]
// where 6 is the number of months at the end of which he can 
// buy the new car and 766 is the nearest integer to '766.158...' .

// Note: Selling, buying and saving are normally done at end of 
// month. Calculations are processed at the end of each considered 
// month but if, by chance from the start, the value of the old 
// car is bigger than the value of the new one or equal there is 
// no saving to be made, no need to wait so he can at the beginning 
// of the month buy the new car:

// nbMonths(12000, 8000, 1000, 1.5) should return [0, 4000]
// nbMonths(8000, 8000, 1000, 1.5) should return [0, 0]


function nbMonths(startPriceOld, startPriceNew, savingperMonth, percentLossByMonth) {
    var numOfMonths = 0;
    var initialCash = startPriceOld;
    while (initialCash < startPriceNew) {
        initialCash += savingperMonth;
        initialCash -= startPriceOld * percentLossByMonth / 100;
        startPriceNew -= startPriceNew * percentLossByMonth / 100;
        startPriceOld -= startPriceOld * percentLossByMonth / 100;
        numOfMonths++;
        if (numOfMonths % 2 !== 0) {
            percentLossByMonth += 0.5;
        } else {
            percentLossByMonth;
        };
    };

    return [numOfMonths, Math.floor(initialCash - startPriceNew)];

};