Essentially APR and EAR are the same but the only difference is when compounding

Question

Essentially APR and EAR are the same but the only difference is when compounding.
For example if the bank charges interest quarterly at 2% on $100.

(1.02)^4= 8.2%

If we were doing year 2

(1.02)^8=17.17%.

So the for 2 years with EAR the interest rate will be 17.17%. If we were figuring out the APR the result would be something like this:


2% x 4= 8%

Year 2

2% x 8= 16%

So the bank will be charging 16% instead of 17.17% because the interest per period is multiplied by the times of periods. The interest rate is the same either charged daily, weekly, monthly, quarterly, or annually. It does have any form of change like in case of EAR.

Explanation / Answer

notes between APR and EAR to remember 1. APR is nominal annual percentage rate while EAR is effective percentage of interest rate. 2. APR can be converted to EAR using EAR= ((1 + i) ^ n) ‘“ 1 but the reversal is not true. 3. At the same percentage rate, APR gives slightly better returns than EAR, factors being constant. 4. APR is simple interest per year minus a fee while EAR is compound interest plus a fee calculated across the year. The mathematical representation for that is FV = (Investment) x ((1 + i) ^ n), where i is the decimal interest rate per compounding period, n is the number of the periods and FV is the future value of the amount that earns interest at i. in the above example, for year 1, this would be $100 x (1.02 ^ 4) = $108.24. The difference between the future value and the investment is the interest. Therefore, for a quarterly compounding, a 8% APR is equivalent to a 8.24% EAR year 2: $100 x (1.02 ^ 8) = $117.17 it looks like you have it down pretty well (:

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