If interest is compounded monthly at 8% per year for 10 years, explain how to find the number of compounding periods and the interest rate per compounding period.
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.
In your case, n = 10x12 = 120 and i = 8/100(12) = .00666...
To find the number of compounding periods, you need to know the time period for which interest is being compounded and the compounding frequency. In this case, the interest is compounded monthly for 10 years.
The number of compounding periods can be calculated by multiplying the number of years by the compounding frequency. In this example, since the interest is compounded monthly for 10 years, the number of compounding periods would be 10 x 12 = 120.
To find the interest rate per compounding period, you need to divide the annual interest rate by the compounding frequency. In this case, the annual interest rate is 8% and the interest is compounded monthly, so the interest rate per compounding period would be 8% / 12 = 0.67%.
So, to summarize:
- The number of compounding periods is 120 (10 years multiplied by 12 months).
- The interest rate per compounding period is 0.67% (8% divided by 12 months).