Let us find the value at age 65 for Emily's deposits and
Withdrawal
PV of 50000 withdrawal for 24 years at age 65 =
50000*(1-(1+r)-n)/r =
50000*(1-(1+11%)-24)/11% = 417,406.83
a) Amount to be set aside = 417,406.83/((1+r)n-1)/r =
417,406.83/(1+11%)20 = 51,772.60
b) PV of 50000 withdrawal for 24 years at age 65 =
50000*(1-(1+r)-n)/r = 50000*(1-(1+8%)-24)/8%
= 526,437.91
Amount to be set aside = 526,437.91/((1+r)n-1)/r =
526,437.91/(1+11%)20 = 65,296.16
c) FV of 75000 at year 65 = 75000*(1+11%)20 =
604673.37
PV of 50000 withdrawal for 24 years at age 65 =
50000*(1-(1+r)-n)/r = 50000*(1-(1+8%)-24)/8%
= 526,437.91
Value at age 65 = 604673.37 - 526,437.91 = 78,235.45
Amount left at age 90 = 78,235.45*(1+8%)25=
535,793.55
Please Discuss in case of Doubt
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