Time value Annuiies Personal Finance Problem Marian Kirk wishes to select the be
ID: 1172442 • Letter: T
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Time value Annuiies Personal Finance Problem Marian Kirk wishes to select the better of two 9-year annuties, C and D Annuity Cis an ardnary Annuity D is an annuity due of $1,710 per year for 9 years annuity of $1,950 per year for 9 years a. Find the future value of both annuites at the end of year 9, b. Use your findngs n part a to ndicate which annuity has the greater future vale at the end of year 9 for both the (1) 11% ad Oza nerest rate. c. Find the present value of both annuities, assurnng that Marian can earn (1) 11% annual nterest and 2) 22% amual interest d. Use your firdngs part c to ndicate which annuity has the greater present value for both the (1) 11% and 2,22% merest raes e. Brety compare, contrast, and explan any dterences between your frangs using te 11% and 22% interest rates in parts b and d assuming that Manan can eam (1) 11% annual interest and (2) 22% annua interest a. The future value of Annuity C at 11% nterest is sü Rund to the nearest cent ) The future value of Arnuty D at 11% interest is $ (Round to the nearest cent) The future value of Annuity Cat 22% interest ist[] (Round to the nearest cent) The future value of Annuity D at 22%nterestis?(Round to the nearest cent) b. Using your findings in part a, which annuity has the greater nare value atthe end of year gat11%nterom select pe best answer below) O Annuity D Using your findings in part a vrtien anuty hasthe greater future vaue at the end of year pat22% nterest? (Select the best anser beli) A Annuity CExplanation / Answer
Answer a.
If Interest Rate is 11%:
Project C:
Future Value = $1,950*1.11^8 + $1,950*1.11^7 + $1,950*1.11^6 + ... + $1,950*1.11 + $1,950
Future Value = $1,950 * (1.11^9 - 1) / 0.11
Future Value = $27,619.75
Project D:
Future Value = $1,710*1.11^9 + $1,710*1.11^8 + $1,710*1.11^7 + ... + $1,710*1.11^2 + $1,710*1.11
Future Value = $1,710 * 1.11 * (1.11^9 - 1) / 0.11
Future Value = $26,884.64
If Interest Rate is 22%:
Project C:
Future Value = $1,950*1.22^8 + $1,950*1.22^7 + $1,950*1.22^6 + ... + $1,950*1.22 + $1,950
Future Value = $1,950 * (1.22^9 - 1) / 0.22
Future Value = $44,206.52
Project D:
Future Value = $1,710*1.22^9 + $1,710*1.22^8 + $1,710*1.22^7 + ... + $1,710*1.22^2 + $1,710*1.22
Future Value = $1,710 * 1.22 * (1.22^9 - 1) / 0.22
Future Value = $47,294.18
Answer b.
If Interest Rate is 11%, Project C has greater future value than Project D.
If Interest Rate is 22%, Project D has greater future value than Project C.
Answer c.
If Interest Rate is 11%:
Project C:
Present Value = $1,950/1.11 + $1,950/1.11^2 + $1,950/1.11^3 + ... + $1,950/1.11^9
Present Value = $1,950 * (1 - (1/1.11)^9) / 0.11
Present Value = $10,797.24
Project D:
Present Value = $1,710 + $1,710/1.11 + $1,710/1.11^2 + ... + $1,710/1.11^8
Present Value = $1,710 * 1.11 * (1 - (1/1.11)^9) / 0.11
Present Value = $10,509.87
If Interest Rate is 22%:
Project C:
Present Value = $1,950/1.22 + $1,950/1.22^2 + $1,950/1.22^3 + ... + $1,950/1.22^9
Present Value = $1,950 * (1 - (1/1.22)^9) / 0.22
Present Value = $7,383.26
Project D:
Present Value = $1,710 + $1,710/1.22 + $1,710/1.22^2 + ... + $1,710/1.22^8
Present Value = $1,710 * 1.22 * (1 - (1/1.22)^9) / 0.22
Present Value = $7,898.95
Answer d.
If Interest Rate is 11%, Project C has greater present value than Project D.
If Interest Rate is 22%, Project D has greater present value than Project C.
Answer e.
If Interest Rate is 11%, we should select Project C.
If Interest Rate is 22%, we should select Project D.
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