<PRE><B>Question 143634</B>
How many months does it take for $1500 to grow to $2000 in an account paying 12% compounded yearly? (Please round your answer to the nearest month.)
:
The interest formula for yearly compound interest:
:
A = P(1+r)^t
where
A = the resulting amt
P = initial amt
r = decimal value of the interest rate
t = no. of yrs
:
1500(1+.12)^t = 2000
:
1.12^t = 2000/1500; divided both sides by 1500
:
1.12^t = {{{4/3}}}
:
log(1.12^t) = log({{{4/3}}}); to log of both sides
:
t*log(1.12) = log({{{4/3}}}); log equiv of exponents
:
.04922t = .12494; the log of both sides
:
t = {{{.12494/.04922}}}
t = 2.54 yrs
:
They want it in months:
12 * 2.54 = 30.48 ~ 30 months
:
:
Check this solution on your calc:
enter: 1.12^2.54 * 1500 ~ 2000, confirms our solution</PRE>