Find the effective rate of interest for 5% compounded monthly.
(1+.05/12)^12 = 1.05116
So, that would be 5.116%
To find the effective rate of interest for 5% compounded monthly, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years
In this case, the annual interest rate is 5% or 0.05, and it is compounded monthly, so n = 12.
Let's assume the principal amount is $1000 and the investment period is 1 year.
A = 1000(1 + 0.05/12)^(12*1)
A = 1000(1 + 0.0041667)^(12)
A = 1000(1.0041667)^(12)
A ≈ 1000(1.051167)
A ≈ 1051.167
The effective rate of interest can be found by subtracting the principal amount from the future value and dividing by the principal amount:
Effective rate of interest = (A - P) / P
Effective rate of interest = (1051.167 - 1000) / 1000
Effective rate of interest ≈ 0.051167 or 5.1167%
Therefore, the effective rate of interest for 5% compounded monthly is approximately 5.1167%.
To find the effective rate of interest for 5% compounded monthly, we first need to understand what it means to compound interest.
Compound interest is the interest that is calculated on both the initial principal amount and any accumulated interest from previous periods. In this case, the interest is compounded monthly, which means it is calculated and added to the principal balance every month.
To calculate the effective rate of interest, we need to consider the compounding frequency, which is monthly in this case. The formula for calculating the effective rate of interest is:
Effective Rate = (1 + (Nominal Rate / Compounding Frequency)) ^ Compounding Frequency - 1
In this case, the nominal rate is 5% and the compounding frequency is monthly. Let's substitute these values into the formula:
Effective Rate = (1 + (0.05 / 12)) ^ 12 - 1
Calculating this equation will give us the effective rate of interest for 5% compounded monthly.