# Thread: Calculating the result of a 5% growth rate over ten years

1. ## Calculating the result of a 5% growth rate over ten years

Hi,

I am curious how I can calculate the total value of an investment if it is expected to grow at 5% annually over the next 10 years.

Right now, assets are at 13.8 trillion and are expected to grow at 5% over the next ten years. What I tried to do was 13.8*0.05=0.69, 0.69*10=6.9, 13.8+6.9=20.7. However, this is wrong, the answer is actually 22.5 trillion and I have no idea why.

Thanks.

2. Originally Posted by pc510
Hi,

I am curious how I can calculate the total value of an investment if it is expected to grow at 5% annually over the next 10 years.

Right now, assets are at 13.8 trillion and are expected to grow at 5% over the next ten years. What I tried to do was 13.8*0.05=0.69, 0.69*10=6.9, 13.8+6.9=20.7. However, this is wrong, the answer is actually 22.5 trillion and I have no idea why.

Thanks.
Have you considered compounded growth?

Suppose the growth rate is 10% and you start with $1000. At the end of the first year you would have (1000 + 10% of 1000 =)$1100

At the end of the second year you would have (1100 + 10% of 1100 =) $1210 At the end of the third year you would have (1210 + 10% of 1210 =)$1331

You'll need to account for "interests" earning "interest"!!

3. Dennis,

Thanks for the formula. This is very helpful. I didn't realize I should be using F=P(1+i)^n.

I have a follow up question. This is quite easy to do with a calculator, but if I were to do this by hand, is there any way to calculate the 1.05^10 how would I do that?

Thank you again!

4. Originally Posted by pc510
...if I were to do this by hand, is there any way to calculate the 1.05^10 how would I do that?
Multiply 1.05 by 1.05 by 1.05 by 1.05 by 1.05 by 1.05 by 1.05 by 1.05 by 1.05 by 1.05, just like the exponent tells you to!

5. Originally Posted by pc510
I have a follow up question. This is quite easy to do with a calculator, but if I were to do this by hand, is there any way to calculate the 1.05^10 how would I do that?
In the days before calculators, we would probably have done this with a slide rule, or with a table of logarithms. Before there were logarithms, there were similar methods using trig tables. In some countries, students still use log tables.

There are also ways to make repeated multiplication a little more efficient, if you had to do it entirely by hand. You might do this:

1.05^2 = 1.1025
1.05^4 = 1.1025^2 = 1.2155 (rounded)
1.05^8 = 1.2155^2 = 1.4774 (rounded)
1.05^10 = 1.05^8 * 1.05^2 = 1.4774*1.1025 = 1.6288 (rounded)

compared to the actual value, 1.62889462677744140625. That took only four multiplications.

Of course, that's mostly for historical interest; but in fact logs might be what you would be using in a computer program, and the last method, called by various names such as "binary exponentiation", is also used in computing.

6. Hi everyone,
Thanks for the replies. Just FYI, I am studying to apply for consulting firms and some jobs expect you to calculate these without a calculator, since one isn't allowed during the test.

Thanks again. This was really helpful.

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