what rate willl an amount double itself in 20 years at simple interest?
(1.00+x)^20 = 2 where x is the percent. If we call 1.00 + x = Y, then
(Y)^20 = 2
20*log(Y) = log 2
20*log(Y) = 0.30103
log Y = 0.30103/2 =
Solve for y and that will tell you what 1+interest rate must be. Subtracting 1.00 will give you the interest rate. I get something like 3.5%
In 20 years you must make one times the original amount in interest.
20 x = 1
x = .05 or 5%
It said simple, not compound.
oops. You're right. I did compound.
To find the rate at which an amount will double itself in 20 years at simple interest, we can use the formula for simple interest:
I = P * r * t
Where:
I = interest earned
P = principal amount (initial amount)
r = interest rate
t = time in years
In this case, we know that the principal amount (P) will double itself, meaning the final amount (A) will be twice the principal amount. So, A = 2P.
We also know that the time (t) is 20 years. Plugging in these values into the simple interest formula, we get:
2P = P * r * 20
Simplifying the equation, we can cancel out the common factor of P:
2 = r * 20
Now, let's solve for the interest rate (r):
r = 2 / 20
r = 0.1
Therefore, the rate at which an amount will double itself in 20 years at simple interest is 0.1, or 10%.