Brooklyn has a goal to save $8,000 to buy a new entertainment system. in order to meet that goal, she deposited $4,132.79 into a savings account. if the account has an interest rate of 4.8% compounded quarterly, approximately when will brooklyn be able to make the purchase?

To see how much interest she'll get after a quarter:

$4132.79 + ($4132.79 × 0.048) = $4331.16

After two quarters:
$4331.16 + ($4331.16 × 0.048) = $4359.06

You can keep going until eventually reaching $8000 then see how many quarters has passed. That's a lot of calculator work!

There's another way that uses less calculation, but more algebra. I call it the exponential formula method! There's this general formula for stuff that increases exponentially, like virus, population, and MONEY:



M is money, d is deposit, t is time taken, and c is just some unknown constant related to the interest rate. There's also the natural logarithm form of this equation, which will come in handy later:



Alright first we gotta find that constant c for this equation to be useful! Let's plug in stuff we know.



We know how much she'll have after one quarter (0.25 years), and we know how much she deposited initially.

After pressing some buttons on the calculator we'll find that c = 0.1875.

Great! Now we can use that formula to find how many years (t) it'll take to reach M=$8000. To save time I'm going to use the natural log form:



That will give us t = 3.522 which means it'll take approximately 3.5 years for her deposit to reach $8000!

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