What equation would i use to find out the actual yearly rate if interest on something? can you explain it to me?
You can use this formula:
Interest = principal * rate * time
I = PRT
would you divide it or multiply it?
* means multiply.
To find the actual yearly rate of interest on something, you would need to use the formula for compound interest. Compound interest is calculated based on the principal amount, the interest rate, and the time period.
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (including the principal and interest)
P = the principal amount (initial amount)
r = the annual interest rate (expressed as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
To find the actual yearly interest rate, you need to solve for "r" in the compound interest formula. Follow these steps:
1. Take the equation A = P(1 + r/n)^(nt) and isolate "r" on one side of the equation.
Divide both sides by P to get: (A/P) = (1 + r/n)^(nt)
2. Take the logarithm (log) of both sides of the equation to bring the exponent down.
log((A/P)) = log((1 + r/n)^(nt))
3. Since log((1 + r/n)^(nt)) is equal to nt × log(1 + r/n), the equation becomes:
log((A/P)) = nt × log(1 + r/n)
4. Solve the equation for "r" by isolating it on one side.
Divide both sides by nt to get:
log((A/P)) / (nt) = log(1 + r/n)
5. To find "r", you need to eliminate the logarithm on the right side of the equation. Take the antilog (inverse logarithm) of both sides to remove the logarithm:
10^(log((A/P)) / (nt)) = 10^(log(1 + r/n))
6. Simplify the equation further:
(A/P) = 10^(log(1 + r/n))^(1/nt)
(A/P) = (1 + r/n)^(1/nt)
7. Rearrange the equation to solve for "r":
(A/P)^(nt) - 1 = r/n
8. Multiply both sides of the equation by n to get the value of "r":
r = n * [(A/P)^(1/nt) - 1]
By substituting the given values of A (final amount), P (principal amount), n (number of compounding periods per year), and t (number of years), you can calculate the actual yearly interest rate (r) using the formula r = n * [(A/P)^(1/nt) - 1].