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

• 12-06-2017, 08:37 AM
pc510
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.
• 12-06-2017, 11:51 AM
Subhotosh Khan
Quote:

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?

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"!!
• 12-06-2017, 01:19 PM
Denis
F = P(1 + i)^n
where:
P = Present value (13.8)
i = interest (.05)
n = number of years (10)
F = Future value (?)
• 12-06-2017, 07:39 PM
pc510
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!
• 12-07-2017, 06:13 PM
stapel
Quote:

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! ;)
• 12-07-2017, 08:37 PM
Denis
Quote:

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?

WHY d'heck would you want to do that?
If your teacher expects such manual calculations,
then you and your classmates should get him/her fired:cool:
• 12-07-2017, 10:31 PM
Dr.Peterson
Quote:

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.
• 12-18-2017, 04:52 AM
pc510
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.