SOLUTION: 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. Round the answer for months up

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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. Round the answer for months up to the nearest multiple of 3
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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%281+%2B+%28r%2Fn%29%29%5E%28nt%29, 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%281+%2B+%28.0813%2F4%29%29%5E%284t%29 = 21000
16000%281.020325%29%5E%284t%29 = 21000
%281.020325%29%5E%284t%29 = 21000%2F16000%29%0D%0A%7B%7B%7B%281.020325%29%5E%284t%29 = 1.3125
Using logs
log%281.020325%29%5E%284t%29 = log(1.3125)
log equiv of exponents
4t*log(1.020325) = log(1.3125)
4t = log1.3125%2Flog%281.020325%29
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