# Compound Interest

1. Jul 4, 2007

### kuahji

At what rate of interest compounded quarterly, to the nearest tenth of a percent, will an investment of $1000 grow to$1500 in 5 years?

I set the problem up 1500=1000(1+x/4)^(4*5)

I then divided by 1000

1.5 = (1+x/4)^20

But this is where I'm stuck.

2. Jul 4, 2007

### ZioX

Well, that's a twentieth degree polynomial.

Just take the 20th root of both sides.

3. Jul 4, 2007

### Dick

Use a logarithm. Get a numerical answer for log(1+x/4). Then exponentiate.

4. Jul 4, 2007

### kuahji

Thanks for the replies, I ended up trying that & got

ln 1.5 = 20 ln (1+x/4)

ln1.5/20 = ln (1+x/4)

1+x/4 = e^.02027

x/4 = .02048

x = .08191 or 8.2%

What kept throwing me off was I kept getting the wrong answer because I kept dividing by four. After doing so many of these problems in a row, thought I was getting confused w/what could be done & couldn't be done regarding logarithms. Thanks again for the help.

5. Jul 4, 2007

### ZioX

$$^{20}\sqrt{1.5}=1+x/4 \mbox{ so that } 4^{20}\sqrt{1.5}-4=x$$

In fact, that's how you can set up a general formula for nominal interest rates.

Last edited: Jul 4, 2007
6. Jul 4, 2007

### Dick

Yes, it's the same thing.

7. Jul 4, 2007

### ZioX

Only because you went around and made exp(.02027)=1.5^(1/20) which was an unnecessary step.

I'm not being adversarial, but the OP should know that there are more tools to use.

Last edited: Jul 4, 2007
8. Jul 5, 2007

### kuahji

Thats pretty interesting, I'm in the logarithm section in pre-calc, so thats why they were used. Good to know that there are other ways to solve the problem as well.

9. Jul 5, 2007

### Dick

I'm not disagreeing. The method using logarithms simply dates from an age when taking a twentieth root wasn't an easy thing. The logs are one way to accomplish that (by turning the root into division).

10. Jul 5, 2007

### ZioX

I just took an actuarial course a couple of semesters ago, and they were able to generate a general formula for variable compounding periods. It utilized mth roots, hence my bias towards them.

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