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Therefore, the future value of your annuity due with $1,000 annual payments at a 5 percent interest rate for five years would be about $5,801.91.
For example, consider a 30-year loan of $200,000 with a stated APR of 10.00%, i.e., 10.0049% APR or the EAR equivalent of 10.4767%. The monthly payments, using APR, would be $1755.87. However, using an EAR of 10.00% the monthly payment would be $1691.78. The difference between the EAR and APR amounts to a difference of $64.09 per month.
The nominal interest rate, also known as an annual percentage rate or APR, is the periodic interest rate multiplied by the number of periods per year. For example, a nominal annual interest rate of 12% based on monthly compounding means a 1% interest rate per month (compounded). [2]
For example, a nominal interest rate of 6% compounded monthly is equivalent to an effective interest rate of 6.17%. 6% compounded monthly is credited as 6%/12 = 0.005 every month. After one year, the initial capital is increased by the factor (1 + 0.005) 12 ≈ 1.0617. Note that the yield increases with the frequency of compounding.
If the above liability (an asset retirement obligation for example) had a discount rate of 10% per annum with annual compounding, the accretion expense for the first 365 days of carrying the liability would be $130, and the PV of the liability as of the end of these 365 days would be $1430.
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In the case of interest rates, a very common but ambiguous way to say that an interest rate rose from 10% per annum to 15% per annum, for example, is to say that the interest rate increased by 5%, which could theoretically mean that it increased from 10% per annum to 10.5% per annum.
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