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

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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
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
i40.tinypic.com/333y62b.png – Jonathan Jan 18 '13 at 21:41

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. - 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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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

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