You invest $25,000 at an annual rate of 7.25% for one year. What is the difference in interest earned if you compound this money on a daily basis instead of an annual basis?
What will be an ideal response?
Answer: For the annual basis, the periodic rate is the same as the annual rate of 7.25%. With a PV of $25,000 and APR of 7.25%, we have 1.0725 times PV equals $26,812.50, rendering an interest earned of $26,812.50 - $25,000 = $1,812.50. For the daily basis, we have C/Y of 365, periodic interest rate = r = 0.019863% (0.00019863). Taking (1 + periodic rate) to the power of C/Y gives: (1.00019863)365 = 1.075185. Multiplying this number by PV gives $26,879.63, rendering an interest earned of $26,879.63 - $25,000 = $1,879.63. Thus, the difference in interest earned is $1,879.63 - $1,812.50 = $67.13.
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