Suppose you are going to receive $13,200 per year for five years. The appropriate interest rate is 8.1 percent.

a-1 What is the present value of the payments if they are in the form of an ordinary annuity?

a-2 What is the present value if the payments are an annuity due?

b-1 Suppose you plan to invest the payments for five years. What is the future value if the payments are an ordinary annuity?

b-2 Suppose you plan to invest the payments for five years. What is the future value if the payments are an annuity due?

a-1) Pv = 52549

a-2) Pv = 56822

b-1) Fv = 77570

b-2 Fv = 83878

Explanation:

b-1) Future value:

S= Sum of amount of annuity=?

n=number of fixed periods=5 years

R=Fixed regular payments=13200

i=Compound interest rate= .081 (suppose annualy)

we know that ordinary  annuity:

S= R [(1+i)∧n-1)]/i

   = 13200[(1+.081)∧5-1]/.081

    =13200(1.476-1)/.081

    = 13200 * 5.8765

  S  = 77570

a.1)Present value of ordinary annuity:

Formula: Present value = C* [(1-(1+i)∧-n)]/i

                                  =13200 * [(1-(1+.081)∧-5]/.081

                                 =13200 * (1-.6774)/.081

                                =13200 * (.3225/.081)

                                =52549

a.2)Present value of ordinary Due:

Formula : Present value = C * [(1-(1+i)∧-n)]/i   *  (1+i)

                                    =  13200 * [(1- (1+.081)∧-5)/.081   * (1+.081)

                                 = 13200  * 3.9822 *  1.081

                               =  56822

b-2) Future value=?

we know that:         S= R [(1+i)∧n+1)-1]/i ]  -R

                             = 13200[ [ (1+.081)∧  5+1 ]-1/.081]   - 13200

                           = 13200 (.5957/.081)   -13200

                         = (13200 * 7.3544)-13200

                         = 97078  -  13200

                       =  83878

the correct answer is:     [c]:     " cyclical unemployment " .