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prisoha [69]
4 years ago
10

How much would you need to deposit in an account now in order to have $6,000 in the account in 8 years? Assume the account earns

6% interest compounded monthly. (could anyone do this whole problem out?
Mathematics
1 answer:
bekas [8.4K]4 years ago
8 0

Answer:

$3,717

Step-by-step explanation:

Hello, in 1 year there are 12 months.

Let's note I the Initial amount.

So, after 1 month we will get the following, because we compute the interest amount for one month only.

I * ( 1 + 6% * (1/12) )

And the next month, we will have interest of the amount available from previous month so it gives

I * ( 1+6\% * \dfrac{1}{12} ) * ( 1+6\% * \dfrac{1}{12} ) \\\\=I*(1+\dfrac{6}{12*100})^2\\\\=I*(1+\dfrac{1}{200})^2\\\\=I*(1.005)^2

... and after n months ...

I*(1.005)^n

8 years is 8*12 = 96 months. so we are looking for I such that

I*(1.005)^{96}=6000\\\\ I =\dfrac{6000}{1.005^{96}}\\\\=\boxed{3717.14345....}

Thank you.

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