You invest $15,000 at an annual rate of 8.25% for one year. What is the difference in interest earned if your investment is compounded on a monthly 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 8.25%. With a PV of $15,000 and APR of 8.25%, we have 1.0825 times PV equals $16,237.50, rendering an interest earned of $16,237.50 - $15,000 = $1,237.50. For the monthly basis, we have C/Y = 12, periodic interest rate r = 0.006875. Taking (1 + periodic rate) to the power of C/Y gives: (1.006865)12 = 1.085692. Multiplying this number by PV gives $16,285.38, rendering an interest earned equal to:
$16,285.38 - $15,000 = $1,285.38. Thus, the difference in interest earned is $1,285.38 - $1,237.50 = $47.88.
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What will be an ideal response?
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