A 6-year annuity with twelve semiannual payments of $7,000 will begin 11 years f

Question

A 6-year annuity with twelve semiannual payments of $7,000 will begin 11 years from now, with the first payment coming 11.5 years from novw If the discount rate is 11 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.) Value of the annuity If the discount rate is 11 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.) Value of the annuity If the discount rate is 11 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.) Value of the annuity

Explanation / Answer

discount rate , r = 11% = 0.11

Effective annual rate , i = ((1+(r/12))12 -1 = ((1+(0.11/12))12 -1 = 0.115719

interest rate semi-annually , x= (1+i)(1/2) -1 = (1.115719)(1/2) -1 = 0.056276 or 5.6276%

amount of semi-annual payment , A = 7000

no.of semi-annual payments, n = no. of years of annuity*2 = 6*2 = 12

value of this annuity 11 years from now = A*PVIFA(12, 5.6276%)

where PVIFA = present value interest rate factor of annuity

PVIFA(12, 5.6276%) =[ (1+x)n -1]/((1+x)n *x)

= [ (1.056276)12 -1]/((1.056276)12 *0.056276) = 8.557693596

value of this annuity 11 years from now, v1 = 7000*8.557693596 = 59903.85517

value of this annuity 5 years from now = v1/((1+x)6 ) = 59903.85517/((1.056276)6 ) = $43,131.07671 or $43,131.08 ( after rounding off)

value of this annuity 3 years from now = v1/((1+x)8 ) = 59903.85517/((1.056276)8 ) = $38657.6523 or $38,657.65 ( after rounding off)

current value of annuity = v1/((1+x)11 ) = 59903.85517/((1.056276)11 ) = $32802.22015 or $32,802.22 ( after rounding off)

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