SOLUTION: I have tried a number of equations and even gone to my school's tutoring center. It is an online preogram so the answer has to be exact, I know it's about 2 but I can't get it to b

Question 68029: I have tried a number of equations and even gone to my school's tutoring center. It is an online preogram so the answer has to be exact, I know it's about 2 but I can't get it to be exact that the program will say it is correct. I hope you can help.
You invest $6000. Your banker tells you that your investment will double in exactly 5 years. At your next party you tell your friends that you invested money (you modestly omit the amount) at _______ percent annual interest. (Enter your percentage with at least three digits beyond the decimal point.)

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
You invest $6000. Your banker tells you that your investment will double in exactly 5 years. At your next party you tell your friends that you invested money (you modestly omit the amount) at _______ percent annual interest. (Enter your percentage with at least three digits beyond the decimal point.)
:
The compound interest equation:
A = Ao(1 + i)^n
or
Ao(1 + i)^n = A
:
Where:
A = the value of the investment after a specific time
Ao = initial amt
i = interest rate per compounding period
n = total number of compounding periods
:
In your problem A = 12000, Ao = 6000, n = 5 years, find i (in decimals)
6000(1 + i)^5 = 12000
:
Divide both sides by 6000
(1 + i)^5 = 2
:
log(1+i)^5 = log(2)
:
use the log equivalent of exponents
5*log(1 + i) = log(2)
:
Find the log of 2:
5*log(1+i) = .30103
;
Divide both sides by 5 and you have:
log(1+i) = .060206
:
Find the anti-log (10^x) of both sides:
1 + i = 1.148698
:
i = 1.148698 - 1
:
i = .148698 is the interest rate in decimals; 14.870% to double your $$ in 5 yr
:
:
Check it in the original formula
A = 6000(1 + .148698)^5
A = 6000(1.148698)^5, use a good calc to find 1.148698^5
A = 6000(2)
A = 12000

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