SOLUTION: You have $1200 to invest in a bank account with interest rate of 4.5% compounded monthly. After how many years will your account total pass $2200. The correct answer is one of t

Algebra ->  Finance -> SOLUTION: You have $1200 to invest in a bank account with interest rate of 4.5% compounded monthly. After how many years will your account total pass $2200. The correct answer is one of t      Log On


   

Question 1199028: You have $1200 to invest in a bank account with interest rate of 4.5% compounded monthly. After how many years will your account total pass $2200.
The correct answer is one of the following. Which one is correct?
A) 12
B) 13
C) 14
D) 15
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

The formula for compound interest is as follows:
A=+P%281+%2B+r%2Fn%29%5E%28n%2At%29
where:
P : principal amount, or initial investment
A : amount after time t
r : interest rate
n+: number of compounding periods, usually expressed in years
t:number of years
given:
P=1200
A=2200
r=0.045
n=12 (compounded monthly)
find:
t=

A=+P%281+%2B+r%2Fn%29%5E%28n%2At%29
we want to know when will be
P%281+%2B+r%2Fn%29%5E%28n%2At%29%3EA
1200%281+%2B+0.045%2F12%29%5E%2812%2At%29%3E2200
%281.00375%29%5E%2812%2At%29%3E2200%2F1200
%281.00375%29%5E%2812%2At%29%3E11%2F6
use log
log%28%281.00375%29%5E%2812%2At%29%29%3Elog%2811%2F6%29

%2812%2At%29log%28%281.00375%29%29%3Elog%2811%2F6%29

12%2At%3Elog%2811%2F6%29%2Flog%28%281.00375%29%29

t%3Elog%2811%2F6%29%2F%2812log%28%281.00375%29%29%29

t%3E13.4949

so,
t=14

account will surpass $2200 after 14 years