Find the number of years it will take for $27,000 to grow to $34262.61 at 6% interest compounded quarterly.

Question

kropot72 · Answer

The following equation is the starting point:
$$34262.61=27000(1+\frac{0.06}{4})^{x}=27000\times (1.015)^{x}$$
Can yhou see what the next step should be?

anonymous · Answer

So...
     34262.61=(27405)^4x 
               ??

campbell_st · Answer

no simplify the 1st equation 

$$34262.61 = 27000(1.015)^x$$

then 

$$\frac{34262.61}{27000} = 1.015^x$$

simplify the above equation 

do you know how to use logarithms...?

anonymous · Answer

It's one of those things if I'm pointed in the right direction I rememebr the way :S

anonymous · Answer

So am I just dividing both sides by 27000?  And then logging it out?

campbell_st · Answer

yes... and with log laws

$$\log(b^a) = alog(b)$$

you need the above law for the right hand side... doesn't matter if its base 10 or base e logs

and simplify the left hand side

log (1.26899) = xlog(1.015)

isolate x 1st then evaluate for the answer

campbell_st · Answer

when you find x.... it will be the number of quarters.... since the investment was compounded quarterly... divide by 4 for the years...

anonymous · Answer

4?

campbell_st · Answer

yes... I got 16 quarters or 4 years

anonymous · Answer

Yeah, x=16
So, I'm dividing that by four because its quarterly

campbell_st · Answer

thats correct.... hope it helps

anonymous · Answer

It does...just need to keep doing them.  The logs have me hung up.  Thank you!