Future Value of an Annuity for Various Compounding Periods. I have been provided
ID: 2772832 • Letter: F
Question
Future Value of an Annuity for Various Compounding Periods. I have been provided the answers but must show ALL WORK IN DETAIL AND FORMULAS.
Find the future values of the following ordinary annuites:
A-- FV of $400 each 6 months for 5 years at a nominal rate of 12%, compounded semiannually.
(Answer is 5, 272.32--show all work and formulas)
B--FV of $200 each 3 months for 5 years at a nominal rate of 12% compounded quartely
(Answer is 5, 374.07--show all work and formulas)
C--The annuities described in parts a and b have the same total amount of money paid into them during the 5-year period and both earn interest at the same nominal rate, yet the annuity in part b earns 101.75 more than the one in part a over 5 years. Why does this occur?--Please explain.
Explanation / Answer
Annual Interest rate 12% Semi Annual interestRate 6% Time in years Opening Balance Interest on Opening Balance Deposit Closing Balance 0.50 - - 400.00 400.00 1.00 400.00 24.000000 400.00 824.00 1.50 824.00 49.440000 400.00 1,273.44 2.00 1,273.44 76.406400 400.00 1,749.85 2.50 1,749.85 104.990784 400.00 2,254.84 3.00 2,254.84 135.290231 400.00 2,790.13 3.50 2,790.13 167.407645 400.00 3,357.54 4.00 3,357.54 201.452104 400.00 3,958.99 4.50 3,958.99 237.539230 400.00 4,596.53 5.00 4,596.53 275.791584 400.00 5,272.32 Annual Interest rate 12% Quarterly interestRate 3% Time in years Opening Balance Interest on Opening Balance Deposit Closing Balance 0.25 - - 200.00 200.00 0.50 200.00 6.000000 200.00 406.00 0.75 406.00 12.180000 200.00 618.18 1.00 618.18 18.545400 200.00 836.73 1.25 836.73 25.101762 200.00 1,061.83 1.50 1,061.83 31.854815 200.00 1,293.68 1.75 1,293.68 38.810459 200.00 1,532.49 2.00 1,532.49 45.974773 200.00 1,778.47 2.25 1,778.47 53.354016 200.00 2,031.82 2.50 2,031.82 60.954637 200.00 2,292.78 2.75 2,292.78 68.783276 200.00 2,561.56 3.00 2,561.56 76.846774 200.00 2,838.41 3.25 2,838.41 85.152177 200.00 3,123.56 3.50 3,123.56 93.706743 200.00 3,417.26 3.75 3,417.26 102.517945 200.00 3,719.78 4.00 3,719.78 111.593483 200.00 4,031.38 4.25 4,031.38 120.941288 200.00 4,352.32 4.50 4,352.32 130.569526 200.00 4,682.89 4.75 4,682.89 140.486612 200.00 5,023.37 5.00 5,023.37 150.701211 200.00 5,374.07 This occurs because compounding is done Quarterly Effective interest rate is higher for Quarterly in comparison to semi Annually
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