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Deposit formula document

question number 24 the treats Jasmine decided to put $100 in a savings account each month the account pays to represent animal interest compounded monthly question how much money s will Jasmine have after one year okay so we're looking at the compounded growth situation where contributions are being made all right so let's start out by writing down the formula for compound interest this is not just our typical compound interest scenario it's um where the interest compounded in times within that within a year but we have contributions being made okay so each month jasmine puts in 100 dollars so let's take a look at the appropriate formula that applies to this scenario okay so let's call it compound interest with contributions okay all right so what we are looking at is what the final amount is after a period of two years okay the final amount as a function of T years is basically the compounded growth compounded growth of the principal okay assuming you started with a specific amount of money plus compounded growth compounded growth of your contributions to contributions are growing and your original principal that you started with is going out so okay now there are two ways that we can express this two formats for the format the exactly the same let's take a look at the first form which is the simplified form form one from one is given by a of T that's the amount final amount is equal to the compounded growth of the principal is basically P times one plus the rate over number of times compounded per year raised to the number of times compounded a year times T so let's say you just put a particular amount of money in a savings account without making any contributions and it's come back compounded the interest is compounded n times per year this formula will suffice okay but we have contributions we made so we have to compensate for that - so that is given by the payments PMT times one plus rate over number of times compounded per year raised to the number of times compounded per year times T - the payment okay that value is divided by the rate divided by the number of times compounded per year okay so this is one form for computing the amount that you have over two years let's take a look at another form it's the same thing but it's not a simple a simplified as form one okay take a look at form two this is the one that we'll be using for this particular problem because upon substitution it arrives at a state that's consistent with the she's provided okay so the component growth of the principal component remains the same we're just gonna alter the second part slightly okay now this can be also written as the payment every month - the payment times 1 plus R over N to the NT so you notice...