SOLUTION: Kindly help me to solve this problem: Ken deposits 6,000 into a saving account at t=0. The account pays simple interest at an annual rate 10%. Ken withdraws the entire balance o

Algebra ->  Finance -> SOLUTION: Kindly help me to solve this problem: Ken deposits 6,000 into a saving account at t=0. The account pays simple interest at an annual rate 10%. Ken withdraws the entire balance o      Log On


   



Question 949971: Kindly help me to solve this problem:
Ken deposits 6,000 into a saving account at t=0. The account pays simple interest at an annual rate 10%. Ken withdraws the entire balance of his savings account at t=12.
Steve deposits 12,000 into a saving account at a later date, t+x. Steve's account pays compound interest at an annual rate of 10%. Steve withdraws the entire balance of his savings account at t=12.
If Steve's account balance is twice that of Kevin's account balance at t=12. what is the value of x? (that is how long after t=0 did Steve make his depose?).

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Ken deposits 6,000 into a saving account at t=0.
The account pays simple interest at an annual rate 10%.
Ken withdraws the entire balance of his savings account at t=12.
Find K's amt at t=12
k = 6000 + 6000*.1*12
k = $13,200
:
Steve deposits 12,000 into a saving account at a later date, t+x.
Steve's account pays compound interest at an annual rate of 10%.
Steve withdraws the entire balance of his savings account at t=12.
If Steve's account balance is twice that of Kevin's account balance at t=12.
what is the value of x? (that is how long after t=0 did Steve make his deposit?)
12000%281.10%29%5E%2812-x%29+=+26400
1.10%5E%2812-x%29+=+26400%2F12000
%281.10%29%5E%2812-x%29+=+2.2
(12-x)log(1.1) = log(2.2)
12-x = log%282.2%29%2Flog%281.1%29
12 - x = 8.2725
-x = 8.2725 - 12
-x = -3.727
x = 3.727 yrs after Ken's deposit which was t=0
:
:
We can check this. Steve's 12000 was in the bank 8.2725 yrs
12000(1.1^8.2725) = 26400