If the bank is quoting an Annual Percentage Rate (APR) of 0.064 compounded quarterly (N=4), what is the Effective Annual Rate for the year in percent (0.052 is 5.2%, so answer 5.2000) ?

Question

BlackTom AI · Accepted Answer

The problem asks for the Effective Annual Rate (EAR) when the bank quotes an APR of 0.064 with quarterly compounding (N=4).

First, determine the periodic rate: since the annual APR is 0.064 and compounding occurs quarterly, the rate per quarter is 0.064 / 4 = 0.016 (i.e., 1.6% per quarter).

Next, apply quarterly compounding to obtain the EAR: EAR = (1 + periodic_rate)^(number_of_periods) - 1 = (1 + 0.016)^4 - 1.

Compute step by step:
- (1 + 0.016) = 1.016
- 1.016^2 = 1.032256
- 1.032256^2 = 1.065552449536
- Subtract 1: 1.065552449536 - 1 = 0.065552449536

Convert to a percentage: 0.065552449536 × 100 = 6.5552449536%

Thus, the exact EAR is approximately 6.5552% when rounded to four decimal places. If someone reports 6.5744%, that value would correspond to a slightly different assumption or rounding path, but with the standard EAR formula and the given APR with quarterly compounding, the calculation above yields about 6.5552%.

Notes and potential pitfalls:
- Do not confuse nominal APR with EAR; EAR accounts for compounding.
- If you instead used a different compounding frequency or different APR convention, you would get a different EAR.
- Small differences may arise from rounding intermediate steps, but the result above is consistent with (1 + 0.064/4)^4 − 1.

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If the bank is quoting an Annual Percentage Rate (APR) of 0.064 compounded quarterly (N=4), what is the Effective Annual Rate for the year in percent (0.052 is 5.2%, so answer 5.2000) ?

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