Compound Interest: Grow $1000 to $1500 in 5 Years?

[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.

 

[ZioX]

Well, that's a twentieth degree polynomial.

Just take the 20th root of both sides.

 

[Dick]

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

 

[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.

 

[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.

 

[Dick]

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

Yes, it's the same thing.

 

[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.

 

[kuahji]

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

 

[Dick]

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.

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).

 

[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.