At what rate percent does compound interest on a sum of money becomes fourfold in 2 years.
4=1(1+i)^2
1+i=2
I= 100 percent
To find the interest rate at which a sum of money becomes fourfold in 2 years, we can use the compound interest formula.
The compound interest formula is given by:
A = P(1 + r/n)^(nt)
Where:
A = final amount (fourfold the original sum)
P = principal amount (initial sum of money)
r = annual interest rate (rate percent we want to find)
n = number of times interest is compounded per year
t = number of years
In this case, we have A = 4P, and t = 2. We need to find r.
Substituting these values into the formula, we get:
4P = P(1 + r/n)^(2n)
Simplifying the equation, we can divide both sides by P:
4 = (1 + r/n)^(2n)
To solve for r, we can take the natural logarithm (ln) of both sides of the equation:
ln(4) = ln[(1 + r/n)^(2n)]
Using the properties of logarithms, we can bring down the exponent and rearrange the equation:
ln(4) = 2n * ln(1 + r/n)
Now, we can isolate the variable r:
r = n * [(e^(ln(4)/(2n))) - 1]
To find the interest rate percent, we multiply r by 100.
So, the final formula to find the interest rate percent is:
Interest Rate Percent = 100 * n * [(e^(ln(4)/(2n))) - 1]
Now you can substitute the value of n (number of compounding periods per year) to calculate the interest rate percent for compound interest.