Compound Interest maths question?

Question

I put $1 in the back today at 8% compound interest pa. How many years will it take me to save up $360 148 329.50?

Can someone tell me how to work out this type of question? Btw the answers meant to be a whole number.

Answer 1

1*.8=.64

1+.64=1.64

1.64*.8=1.312

1.64+1.312=2.15168

You basically keep doing that untill you get $360 148 329.50

Answer 2

1.08^n = 360,148,329.50

n ln 1.08 = ln 360,148,329.50

n = 256

256 years.

EDIT: each year, you have 1.08 times the last year. So after 2 years, you have 1.08 * 1.08 = 1.08² and after n years, 1.08^n. Now, let T be the total amount you want. Then we wish to find n where 1.08^n = T. Taking the the natural log of both sides:

ln (1.08^n) = ln T

{by the property of logs, log (a^b) = b log a}

n ln 1.08 = ln T

n = ln T / ln 1.08