Question

You deposit $500 in an account earning 4% coumpound interest for 6 years. find the future value and the interest earned for each of the following compounding frequencies. use the bankers' rule for daily compounding (i.e., 360 days in a year).

Answer 1

To find the future value and interest earned for each compounding frequency, use the compound interest formula. For annual, semi-annual, and daily compounding (using Bankers' rule), the future values and interest earned are $598.85 and $98.85, $600.69 and $100.69, and $601.03 and $101.03, respectively.

Step-by-step explanation:

To find the future value and interest earned for each of the compounding frequencies, we can use the formula for compound interest which is:

Future Value = Principal × (1 + (Interest Rate / Number of Compounding Periods))^(Number of Compounding Periods × Number of Years)

For each of the compounding frequencies:

1. Annual compounding: Future Value = $500 × (1 + (0.04 / 1))^(1 × 6) = $598.85. Interest Earned = Future Value - Principal = $598.85 - $500 = $98.85.
2. Semi-annual compounding: Future Value = $500 × (1 + (0.04 / 2))^(2 × 6) = $600.69. Interest Earned = Future Value - Principal = $600.69 - $500 = $100.69.
3. Daily compounding (using the Bankers' rule): Future Value = $500 × (1 + (0.04 / 360))^(360 × 6) = $601.03. Interest Earned = Future Value - Principal = $601.03 - $500 = $101.03.