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How much money should I save in an account paying 5% interest compounded monthly if I want to have $ 6,000 in 6 months ?

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2  
Find the correct formula, then plug and chug. –  Calvin Lin Jan 18 '13 at 21:25
    
Are you saving each month, too, or are you putting a lump sum into the account at the beginning of the six months? –  Thomas Andrews Jan 18 '13 at 21:29
5  
where are you getting an interest rate like that?? –  Jonathan Jan 18 '13 at 21:37
    
@Jonathan Meh, just wanted to ask that... –  CBenni Jan 18 '13 at 21:39
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i40.tinypic.com/333y62b.png –  Jonathan Jan 18 '13 at 21:41

3 Answers 3

Using the formula:

$$A = p(1 + \frac{r}{n})^{nt}$$

where:

$\bullet$ $A$ = Amount = 6000

$\bullet$ $r$ = Rate = 5 % = 0.05

$\bullet$ $t$ = Time = 6 months

$\bullet$ $n$ = Monthly = 12

$\bullet$ $p$ = Principal = Unknown

We have:

$$6000 = p(1 + \frac{.05}{12})^{72}$$

Solving yields $p = \$4447.68$

Regards.

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2  
Actually, in the US at least, the "5% compounded monthly" usually means $n=12$. But that might be a regionalism –  Thomas Andrews Jan 18 '13 at 21:40
    
@ThomasAndrews: I started with it that way and changed it! Thanks and regards! –  Amzoti Jan 18 '13 at 21:48
    
Seems students get tripped up with these kinds of questions when first learning interest/compounding, etc.! Good work! –  amWhy May 8 '13 at 1:10
    
@amWhy: Agreed and the financial industry doesn't help by creating every imaginable permutation! ;-) –  Amzoti May 8 '13 at 1:12

Recall the formula for compound interest:

$$\text{Initial}\times(1+\text{Increase})^{n},$$

Where $n$ is the number of months. So in this case we have $\text{Increase}=0.05$, $n=6$ and we are trying to find $\text{Initial}$. Algebraically:

$$\text{Initial}\times1.05^{6}=\$6,000 \implies \text{Initial}=\frac{\$6,000}{1.05^{6}}=\$4,477.29$$

I hope this helps!

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3  
Usually, "5% compounded each month" really means "5%/12 each month, compunded." That is, the "5%" is a yearly number. At least here in the USA. –  Thomas Andrews Jan 18 '13 at 21:30

$$ 6000 = P (1.05)^6 \implies P = \frac{6000}{(1.05)^6} $$

Run that through your calculator.

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