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Future Value Compute the future value in year 10 of a $3,000 deposit in year 1 a

ID: 2734629 • Letter: F

Question

Future Value Compute the future value in year 10 of a $3,000 deposit in year 1 and another $4,500 deposit at the end of year 4 using a 10 percent interest rate. Present Value Compute the present value of a $3,000 deposit in year 2 and another $4,500 deposit at the end of year 5 using 6 percent interest rate. Present Value of a Perpetuity What's the present value a bond issued by UK Treasury with par value of 1000 pound, that promised to give investor 50 pounds per year forever, if interest rate is 4 percent? Present Value of an Annuity Due If the present value of an ordinary, 10-year annuity is $10,500 and interest rate is 6.5 percent. What is the present value of the same annuity due? Effective Annual Rate A loan is offered with monthly payments and an 8 percent APR. What's the loan's effective annual rate (EAR)?

Explanation / Answer

1.Future value :

                     Assume that deposit was made at the begining of the year 1.

              Future value of deposit of $3000 = $3000*(1.10) power10

                                                             = 7781.22

           Future value of deposit of $4500 at the end of 4th year = $4500*(1.10)power 4

                                                                                          = $6588.45

2.Present value:

        Present value of $3000 in year at 6% = $3000*(0.9434)

                                                              = $2830 (at begining of 2nd year)

        Present value of $4500 at the end of 5th year = $4500*0.7472

                                                                          = $3362.66

3.Present value of perpetuity :

                    since there is a fixed payment of 50 pounds and rate of interest of 4%.

                       present value of perpetuity = 50/0.04

                                                              = 1250

4.Present value of an annuity due :

                        Formula for present value of annuity =(1+r)*p{1-1/(1+r)power to n/r)

                                                                = (1+0.065)*10500{1-1/1.065power to 10/0.065)

                                                                = $80387.26(approximately)

5.Effective Annual rate :

          EAR is used to determine the actual annual rate that would be paid on a loan or investment if the stated annual rate is affected by compounding.

                     =8.3% ((1+0.08/12)power to 12-1)