convert interest semi-annually compouding to monthly compounding?

Question

The question reads: The interest rate is quoted 5% per annum with semi-annual compounding. What is the equivalent rate with monthly compounding.
I need to know how to calculate the interest rate.

Answer 1

If the rate S compounds semi-annually, then the APR is:

APR = (1+S/2)^2 - 1

If the rate M compounds monthly, then the APR is:

APR = (1+M/12)^12 - 1

Since you want a monthly rate that has the same APR as the semiannual rate, then you get:

(1+S/2)^2 = (1+M/12)^12

(1.025)^2 = (1+M/12)^12

(1.025)^(1/6) = 1+M/12

M = 4.9487%

Answer 2

For the best answers, search on this site https://shorturl.im/axsWB

The two statements you have in quotes mean the same thing. Interest rates are stated in terms of a year; compounding semi-annually means it pays interest twice a year. To figure the period rate you divide the yearly rate by how many times it compounds within one year. In this example, it pays twice a year so you divide the rate by 2. The rate of interest paid at every six-month interval would be 2.5%. To have a periodic interest of 5% the statement would say 10% interest compounded semi-annually. Hope that helps.

Answer 3

If you need to convert semi annual interest payments into annual:

simply take the formulas and make them balance each other and solve for the unknown.

if we have a semi annual rate of 8% and we need it to be converted to annual:

(1+0.08/2)^2 = (1 + x)
1.0816= (1+x)
x=(1.0816)-1
x=0.0816 or 8.16 % annually.

if it is monthly then the right hand side would be (1+x/12)^12 and solve for x or whatever you want to call it.(Rm, K, M)

Answer 4

It means the amount you deposit earns an annual rate of 5% interest for six months, then the interest is credited to the account and the sum of principal and interest earns at an annual rate of 5% interest for the next six months. For example, let's say you deposit $100. In six months, $2.50 is credited to the account. For the next six months, you earn interest on $102.50 at the annual rate of 5%. At the second six-month interval, $2.56 is credited, and you have a total of $105.06. The $.06 is what you earned from the semi-annual compounding. If you were earning simple interest at 5%, then you would only have $105 after one year's earnings.