Question

A deferred annuity consists of an ordinary annuity paying $2100 semiannually for a 12-year term after a 6-year period of deferral. Calculate the deferred annuity’s present value using a discount rate of 4.1% compounded quarterly. (Do not round intermediate calculations and round your final answer to 2 decimal places.)

   

Present value

$

Answer 1

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

A B с D 1 2 Deferral period in years 6 3 4 Semi-annual payment APR, compounded quaterly Effective semi-annual rate Term in years No. of semi-annual payment $2,100.00 4.10% 2.06% 12 24 5 6 7 8 9 10 11 12 13 14 Value of semi-annual payement at Year-6 $39,448.34 Present value of deferral annuity $30,884.18 15

Cell reference -

А. B с 1 Deferral period in years 6 N 3 4 3 4 5 LC Semi-annual payment APR, compounded quaterly Effective semi-annual rate Term in years No. of semi-annual payment 2100 0.041 = (1+C5/4)^2-1 12 =C7*2 7 8 9 10 Value of semi-annual payement at Year-6 =PV(C6,08,-C4,0) 11 Present value of deferral annuity =C10/(1+C6)^(C2*2) 12 13 14 15

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