A 6-year annuity of twelve $11,800 semiannual payments will begin 9 years from n

Question

A 6-year annuity of twelve $11,800 semiannual payments will begin 9 years from now, with the first payment coming 9.5 years from now.

   

If the discount rate is 12 percent compounded monthly, what is the value of this annuity five years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

   

     

If the discount rate is 12 percent compounded monthly, what is the value three years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

    

     

If the discount rate is 12 percent compounded monthly, what is the current value of the annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

     

A 6-year annuity of twelve $11,800 semiannual payments will begin 9 years from now, with the first payment coming 9.5 years from now.

Explanation / Answer

12% monthly compounding APR can be converted into semi-annual compounding APR as shown below.

= [(1+1%)^6-1]×2

= 12.30%

Value of equity 9 year from now P×[1-(1÷(1+r)^n)]÷r Here, 1 Interest rate per annum 12.30% 2 Number of years                                                                      6 3 Number of compoundings per per annum                                                                      2 4 = 1÷3 Interest rate per period ( r) 6.15% 5 = 2×3 Number of periods (n) 12 Payment per period (P) $                                                 11,800.00 Value of equity 9 year from now $                                                       98,121.86 11800*[1-(1/(1+6.15%)^12)]/6.15%

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