Determine the effective interest rate if money is worth 18% compounded monthly.Give your answer to two decimal places.
r=effective interest rate
i=stated interest rate(18%)
n=number of compounding periods
therefore:r={(1+i/n)^n - 1}
i=0.18
n=12
r={(1+0.18/12)^12 - 1}
r=0.20
To determine the effective interest rate, we need to use the formula for compound interest:
A = P * (1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment/loan amount
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years
In this case, we are given that the annual interest rate is 18% and it is compounded monthly. So, let's calculate the effective interest rate:
r = 18% / 100 = 0.18 (annual interest rate as a decimal)
n = 12 (compounded monthly)
Using the formula:
A = P * (1 + r/n)^(nt)
We want to find the value of (1 + r/n)^(nt), which represents the multiplier of the principal amount. Let's assume we start with a principal amount of $1.
A = $1 * (1 + 0.18/12)^(12*1)
A = $1 * (1.015)^12
A = $1 * 1.19561892921
A ≈ $1.20 (rounded to two decimal places)
Therefore, the effective interest rate is 20% when money is worth 18% compounded monthly.