SOLUTION: How long will it take for an investment to reach 4 times its original value if it is invested at 9.3% APR compounded monthly? compounded continuosly?

Question 22114: How long will it take for an investment to reach 4 times its original value if it is invested at 9.3% APR compounded monthly? compounded continuosly?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Compound interest formula: A = P(1+r/n)^(nt)
A is amount you have now; P is amount you invested; r is annual
interest rate; n is # of times compounded yearly; t is number of years.
Let "x" be the amount invested and compounded monthly.
Then "4x" is the amount you will have if it reaches 4 times it original value.
So, 4x = x(1+0.093/12)^(12t)
4 = (1.00775)^12t
Take the log of both sides to get the variable out of the exponent.
log(4) = (12t)(log(1.00775)
Solve for "t":
t = (1/12)[log4/log(1.00775)]
t = (1/12)(179.57)
t = 14.96 years
If compounded continuously the formula is A = Pe^rt
In your case 4x = (x)e^(0.093)t
Take the natural log of both sides after cancelling the "x's" to get:
ln(4) = 0.093t
t = [ln4]/0.093
t = 14.91 years
Cheers,
stan H.
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