John was injured in an accident and the insurance company has offered him the choice of $37,000 per year for 15 years with the first payment being made today or a lump sum to be paid off today if they required rate of return is 7.5% what should be the present value of this lump sum amount be today
given data
the insurance company has offered him $37000 per year for 15 years
the present value of lump sum today is needed is = FV/(1+i)n
FV = 37000
n = 15 years
by substituting the values
PV = 37000/(1+0.075)1+37000/(1+0.075)2+37000/(1+0.075)3+37000/(1+0.075)4+37000/(1+0.075)5+37000/(1+0.075)6+37000/(1+0.075)7+37000/(1+0.075)8+37000/(1+0.075)9+37000/(1+0.075)10
PV = 37000/1.075 +37000/1.155625+37000/1.2422968 +37000/1.335469140+37000/1.43562932+37000/1.54330152+37000/1.65904914+37000/1.78347782+37000/1.91723866+37000/2.06103156+37000/2.215608929+37000/2.381779598+37000/2.560413068+37000/2.75244404+37000/2.95887735
PV = 34418.60+32017.30+29783.54+27705.61+25772.66+23974.57+22301.93+20745.98+19298.58+17952.17+16699.69+15534.60+14450.79+13442.59+12504.74
PV = 326603.35
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