When calculating semi-compounded annual rates, why do we have to root it to the power of 1/6?
This is a formula for monthly interest (mortgages) that I found in my older notes.
Monthly interest (mortgages) = (r/2)^1/6
r = interest rate of mortgage in decimal form
it is divided by 2 due to compounding semi-annually
I was thinking.. does 6 mean 6 months?
Compound Interest
With compound interest, the interest due and paid at the end of the interest compounding period is added to the initial starting principal to form a new principal, and this new principal becomes the amount on which the interest for the next interest period is based. The original principal is said to be compounded, and the difference between the the final total, the compound amount, accumulated at the end of the specified interest periods, and the original amount, is called the compound interest.
In its most basic use, if P is an amount deposited into an account paying a periodic interest, then Sn is the final compounded amount accumulated where
..........................Sn = P(1+i)^n
where i is the periodic interest rate in decimal form = %Int./(100m), n is the number of interest bearing periods, and m is the number of interest paying periods per year.
For example, the compound amount and the compound interest on $5000.00 resulting from the accumulation of interest at 6% annual interest compounded monthly for 10 years is as follows:
Since m = 12, i = .06/12 = .005. Since we are dealing with a total of 10 years with 12 interest periods per year, n = 10 x 12 = 120. From this we get
.........................Sn = $5000(1+.005)^120 = $5000(1.8194) = $9097.
Consequently, the compound interest realized is $9097 - $5000 = $4097. Of course the compound interest rate can be calculated directly from the simple expression
.........................I = P[(1+i)^n - 1]
