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What is the future value of a 5-year ordinary annuity of $1000 if the appropriate interest...

  1. What is the future value of a 5-year ordinary annuity of $1000 if the appropriate interest rate is 5%? What is the present value of the annuity?
  2. What is the future value of $1000 after 4 years under 10% annual compounding? Semiannual compounding? Quarterly compounding? Monthly compounding? Daily compounding
  3. What is the effective annual rate (EAR or EFF%)? What is the EFF% for a nominal rate of 5%, compounded semiannually? Compounded quarterly? Compounded monthly? Compounded daily?

Solutions

Expert Solution

Solution:-

A. First we need to calculate Future Value of Ordinary Annuity-

Future Value =

Future Value =

Future Value =

Future Value = $5,525.63

To calculate Present Value of Ordinary Annuity-

Present Value =

Present Value =

Present Value =

Present Value = $4,329.48

B. Future Value if Annually Compounded-

Future Value =

Future Value =

Future Value = $1,464.10

Future Value if Semi-Annually Compounded-

Future Value =

Future Value =

Future Value = $1,477.46

Future Value if Quarterly Compounded-

Future Value =

Future Value =

Future Value = $1,484.51

Future Value if Monthly Compounded-

Future Value =

Future Value =

Future Value = $1,489.35

Future Value if Daily Compounded-

Assume their is 365 days in a year

Future Value =

Future Value =

Future Value = $1,491.74

C. Effective Annual Rate when Compounded Semiannually-

Effective Annual Interest Rate =

Effective Annual Interest Rate =

Effective Annual Interest Rate = 5.0625%

Effective Annual Rate when Compounded Quarterly-

Effective Annual Interest Rate =

Effective Annual Interest Rate =

Effective Annual Interest Rate = 5.0945%

Effective Annual Rate when Compounded Monthly-

Effective Annual Interest Rate =

Effective Annual Interest Rate =

Effective Annual Interest Rate = 5.1162%

Effective Annual Rate when Compounded Daily-

Effective Annual Interest Rate =

Effective Annual Interest Rate =

Effective Annual Interest Rate = 5.1267%

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jeff jeffy answered 1 year ago
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