Question 1040131
 jimmy invest 16000 in an account that pays 8.13% compounded quarterly.
 How long(in years and months) will it take for his investment to reach 21000.
:
the compound interest formula 
{{{A = p(1 + (r/n))^(nt)}}}, where
A = the resulting amt after t yrs
P = initial amt
r = annual interest rate in decimal form
n = compounding periods per yr
t = no. of yrs
:
In the problem
A = 21000
p = 16000
n = 4 (time per yr)
r = .0813
t = yrs
:
{{{16000(1 + (.0813/4))^(4t)}}} = 21000
{{{16000(1.020325)^(4t)}}} = 21000
{{{(1.020325)^(4t)}}} = {{{21000/16000)
{{{(1.020325)^(4t)}}} = 1.3125
Using logs
{{{log(1.020325)^(4t)}}} = log(1.3125)
log equiv of exponents
4t*log(1.020325) = log(1.3125)
4t = {{{log1.3125/log(1.020325)}}}
use you calc
4t = 13.515
divide by 4
t = 3.379 yrs
find the no. of months
.379(12) = 4.54 months
Rounds up to 4 yrs 9 months