SOLUTION: I am confused to which formula to use to solve the following After what time will the interest on a certain sum of money at 10% per annum be half of the intial amount. I have

Question 314555: I am confused to which formula to use to solve the following
After what time will the interest on a certain sum of money at 10% per annum be half of the intial amount.
I have the rate at 10% and know that I need to find the principal and know that the initial amount will be half.
Do I do time / rate?
0.5 / 0.1 = 5 years?
Help!!

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
After what time will the interest on a certain sum of money at 10% per annum be half of the intial amount.
.
Let P = initial amount
then
"principal plus half the amount" = P + .5P = P(1 + .5) = 1.5P
.
Annual compound interest formula:
M = P( 1 + i )^t
where
M is amount (principal plus interest) after time t
P is initial amount (principal)
i is interest
t is time
.
In your case
M = 1.5P
P = p
i = .10
plugging it in:

dividing both sides by P:

take the log base 1.10 of both sides:

using "change of base"

years

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