SOLUTION: An initial investment is made at 4.5% interest, compounded semi annually, how long will it take to become 4 times the original amount? Is this question even possible without th

Question 141443: An initial investment is made at 4.5% interest, compounded semi annually, how long will it take to become 4 times the original amount?
Is this question even possible without the amount of the initial investment?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
An initial investment is made at 4.5% interest, compounded semi annually, how long will it take to become 4 times the original amount?
:
Using the formula; A = P(1+(i/n))^nt
where
A = resulting amt
P = initial amt
i = interest in decimals
n = no. of time per year
t = no. of yrs
:
In this problem we just assign a value of 1 for P and 4 for A:
It asks how long so we solve for t:
:
1(1 + (.045/2))^2t = 4
:
(1+.0225)^2t = 4
:
(1.0225)^2t = 4
:
log(1.0225^2t) = log(4)
:
Log equiv of exponents
2t*log(1.0225) = log(4)
:
Find the logs:
2t*.0096633 = .60206
2t =
2t = 62.3
t =
t = 31.15
So we have to say it will take 31.5 yrs for your money to quadruple at 4.5%, semiannually
:
:
Check solution on a calc: enter: (1.0225)^(2*31.5) = 4.06
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