Assuming that you invest $10,000 in the U.S., how long (to the nearest year) must you wait before your investment is worth $13,000 if the interest is compounded annually at 5.3%?

Question

riley · Answer

so far i've gotten

13,000 = 10,000e^(0.53)t

13,000/10,000 = e^(0.53)t

riley · Answer

but then after that i think I keep messing up somewhere b/c I'm not coming up with the correct answer >_<

anonymous · Answer

X = 1.053^t * 10,000

13,000 = 1.053^ t*10,000

1.053^t = 13,000 / 10,000

1.053^t = 1,3

t = log (1.3) / log (1.053 )

t = 5 years

riley · Answer

Thats the right answer, but I don't get how you got the 1.053? O.O

anonymous · Answer

you get 5.3% interest every year, so every year your investment is multiplied by 1.053

(try 100, 100 * 1.053 = 105.3 => 105.3 - 100 = 5.3 )

anonymous · Answer

10% = 1.1
53% = 1.53
2.1% = 1.021

riley · Answer

oh wow, I was doing that totally wrong then just b/c I was messing the decimal up omg!!

riley · Answer

And I completely get how you did all the other math to it, ty so very much! Now I understand where I was making my mistakes at.  Ty again for explaining it like that. :)

anonymous · Answer

You're welcome :)