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You are considering three alternative banks in which to open a savings account
You are considering three alternative banks in which to open a savings account. The first bank offers you an annual rate r?, and the interest is paid monthly. The second bank offers a rate r2, and the interest is paid daily. The third bank offers a rate ry, and it offers continuous compounding. Give all answers to four decimal places.
Part 1 (1 point) X Feedback See Hint Suppose you were to save $500.0000 in the first bank. The interest rate is ri = 7.0000%. Three years from now, you should have $ * 616,462.79 Part 2 (1 point) X Feedback See Hint Suppose you were to save $500.0000 in the second bank. The interest rate is r2 = 4.0000%. Three years from now, you should have $ X 563,744.72 Part 3 (1 point) X Feedback See Hint Suppose you were to save $500.0000 in the third bank. The interest rate is r3 = 1.0000%. Three years from now, you should have $ X 515,227.27
Expert Solution
1) Interest rate compounded monthly = 7%
Annual effective rate of interest: [1 + (7% / 12)^12 - 1] * 100 = 7.22%
Amount of 500,000 become 500,000 * (1 + 0.0722)^3 = 616,462.79 after 3 years
2) Interest rate compounded daily = 4%
Annual effective rate of interest: [1 + (4% / 365)^365 - 1] * 100 = 4.08%
Amount of 500,000 become 500,000 * (1 + 0.0408)^3 = 563,744.72 after 3 years
3) Interest rate compounded continuous = 1%
Annual effective rate of interest: [e^1% - 1] * 100 = 1.005% where value of e = 2.71828
Amount of 500,000 become 500,000 * (1 + 0.01005)^3 = 515,227.27 after 3 years
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