How long would it take to double your money at 15.86 percent with interest compounded annually?
let the time be n
1(1.1586)^n = 2
log both sides
log 1.1586^n = log2
n(log1.1586) = log 2
n = log2/log1.1586 = appr 4.7 years
To determine how long it would take to double your money at 15.86 percent interest compounded annually, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money at the end of the investment period
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = the number of years
In this case, you want to find the time it takes for the principal amount to double (A = 2P), so the formula can be rearranged:
2P = P(1 + r/n)^(nt)
Dividing both sides of the equation by P, we get:
2 = (1 + r/n)^(nt)
Taking the natural logarithm of both sides of the equation, we can solve for t:
ln(2) = nt * ln(1 + r/n)
Substituting the values we have:
ln(2) = t * ln(1 + 0.1586/1)
Simplifying:
ln(2) = t * ln(1.1586)
Now, we can solve for t by dividing both sides of the equation by ln(1.1586):
t = ln(2) / ln(1.1586)
Using a calculator, we can find:
t ≈ 4.51 years
Therefore, it would take approximately 4.51 years to double your money at 15.86 percent interest compounded annually.
To find out how long it would take to double your money at a given interest rate with compounding, you can use the formula for compound interest. The formula is:
A = P * (1 + r/n)^(n*t)
Where:
A = the final amount (double the initial amount in this case)
P = the principal (initial amount)
r = the interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the time (in years)
In this case, you want to double your money, so A is twice the initial amount. Let's call the initial amount P, so A = 2P. The interest rate is 15.86% or 0.1586 in decimal form. And since interest is compounded annually, n = 1.
Plugging these values into the formula, we have:
2P = P * (1 + 0.1586/1)^(1*t)
Simplifying the equation:
2 = (1 + 0.1586)^t
Now, we need to solve for t. We can take the logarithm of both sides to isolate t:
log(2) = log((1 + 0.1586)^t)
Using the logarithm properties, we can bring down the exponent:
log(2) = t * log(1 + 0.1586)
Now, we can divide both sides by log(1 + 0.1586) to solve for t:
t = log(2) / log(1 + 0.1586)
Using a calculator, the approximate value of t is 4.45 years.
Therefore, it would take approximately 4.45 years to double your money at an interest rate of 15.86% with interest compounded annually.