Answer:
A. $51,772.60
B. $65,296.16
C. $535,793.5
Explanation:
a. Calculation for The amount Emily must set aside now
First step is to calculate the present value of the amounts of 50,000 that was withdraw for 24 years at age 65
Present Value of 50,000 = 50,000*(1-(1+11%)^-24)/11%
Present Value of 50,000 = 417,406.83
Now let calculate the Amount to be set aside
Amount set aside = 417,406.83/(1+11%)^20
Amount set aside= $51,772.60
Therefore The amount Emily must set aside now is $51,772.60
b) Calculation for The amount Emily needs to set aside to achieve her goal
First step is to calculate the present value of the amounts of 50,000 that was withdraw for 24 years at age 65
Present Value of 50,000 = 50,000*(1-(1+8%)^-24)/8%
Present Value of 50,000 = 526,437.91
Now let calculate the Amount to be set aside
Amount set aside = 526,437.91/(1+11%)^20
Amount set aside = $65,296.16
Therefore The amount Emily needs to set aside to achieve her goal is $65,296.16
c) Calculation for The amount that will be left in the account for her heirs
First step is to calculate the Face Value of 75,000 at year 65
Face Value of 75,000 = 75,000*(1+11%)^20
Face Value of 75,000= 604,673.37
Second step is to calculate the present value of the amounts of 50,000 that was withdraw for 24 years at age 65
Present value of 50,000= 50,000*(1-(1+8%)^-24)/8%
Present value of 50,000 = 526,437.91
Third step is to calculate the Value at age 65
Value at age 65 = 604,673.37 - 526,437.91
Value at age 65= 78,235.45
Last step is to calculate the Amount left at age 90
Amount left = 78,235.45*(1+8%)^25
Amount left = $535,793.5
Therefore The amount that will be left in the account for her heirs is $535,793.5
