Answer:
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
