Kay owns two annuities that will each pay $500 a month for the next 12 years. One payment is received at the beginning of each month while the other is received at the end of each month. At a discount rate of 7.25 percent, compounded monthly, what is the difference in the present values of these annuities

The difference in the present values of these annuities is$290

Explanation:

Payment of fixed amount for a fixed period of time on a fixed rate of return is called annuity.

Immediate Payment of fixed amount for a fixed period of time on a fixed rate of return is called advanced annuity.

According to given data

P = monthly payment = $500 every month

r = interest rate = 7.25% per year = 7.25 / 12 = 0.6042% = 0.006042

n = number of period = 12 years x 12 month a year = 144 periods

First Annuity

PV of annuity = P x [ ( 1- ( 1 + r )^-n ) / r ]

PV of annuity = $500 x [ ( 1- ( 1 + 0.006042 )^-144 ) / 0.006042 ]

PV of annuity = $47,995

First Annuity

PV of annuity = P x [ ( 1- ( 1 + r )^-(n-1) ) / r ] + P

PV of annuity = $500 x [ ( 1- ( 1 + 0.006042 )^-(144-1) ) / 0.006042 ] + $500

PV of annuity = $500 x [ ( 1- ( 1 + 0.006042 )^-(143) ) / 0.006042 ] + $500

PV of annuity = $48,285

Difference  = $48,285 - $47,995 = $290

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