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Use nominal rate 4.8% compounded monthly:
(1) James and Jane retire with $500,000 in their retirement account. If they want that to last for 25 years, how much can they take out each month.
(2) Nick and Nora are 30 and intend to retire at age 65; they are just starting a retirement plan. How much must they deposit each month so that after retirement, they can draw out $3,500 each month for 20 years?
(3) Mick and Moira are 30 and intend to retire at age 65; they are just starting a retirement plan. How much must they deposit each month so that after retirement, they can take out $30,000 for a wild vacation and then draw out $3,500 each month for 20 years?
PVIFA= Present Value Interest Factor for an Annuity
It can be read from tables or calculated using the following equations
PVIFA( n, r%)= =[1-1/(1+r%)^n]/r%
Use nominal rate 4.8% compounded monthly:
(1) James and Jane retire with $500,000 in their retirement account. If they want that to last for 25 years, how much can they take out each month.
We have the present value of an annuity
We have to calculate the annuity (equal payments spaced equally in time)
Frequency= M Monthly
No of years= 25
No of Periods= 300
Discount rate annually= 4.80% annual
Discount rate per period= 0.4000% Monthly
n= 300
r= 0.40%
PVIFA (300 periods, .4% rate ) = 174.520995
Present value= 500,000
Therefore, annuity= $2,864.98 =500000/174.520995
Answer: They can take out $2,864.98 each month for 25 years
(2) Nick and Nora are 30 and intend to retire at age 65; they are just starting a retirement plan. How much must they deposit each month so that after retirement, they can draw out $3,500 each month for 20 years?
We first find out the present value of $3,500 each month for 20 years
Frequency= M Monthly
No of years= 20
No of Periods= 240
Discount rate annually= 4.80% annual
Discount rate per period= 0.4000% Monthly
n= 240
r= 0.40%
PVIFA (240 periods, .4% rate ) = 154.093303
Annuity= 3,500
Therefore, present value= 539,326.56 =3500x154.093303
This is the future value that must accumulate in the account
We have to find the annuity (each month for 35 years- from age 30 to 65) that would give us this amount
Frequency= M Monthly
No of years= 35
No of Periods= 420
Discount rate annually= 4.80% annual
Discount rate per period= 0.4000% Monthly
n= 420
r= 0.40%
FVIFA (420 periods, .4% rate ) = 1086.901432
Future value= 539,326.56
Therefore, annuity= 496.21 =539326.56/1086.901432
Answer: Nick and Nora must deposit $496.21 each month
(3) Mick and Moira are 30 and intend to retire at age 65; they are just starting a retirement plan. How much must they deposit each month so that after retirement, they can take out $30,000 for a wild vacation and then draw out $3,500 each month for 20 years?
We first find out the present value of $3,500 each month for 20 years
Frequency= M Monthly
No of years= 20
No of Periods= 240
Discount rate annually= 4.80% annual
Discount rate per period= 0.4000% Monthly
n= 240
r= 0.40%
PVIFA (240 periods, .4% rate ) = 154.093303
Annuity= 3,500
Therefore, present value= 539,326.56 =3500x154.093303
In addition to this annuity, they also require $30,000
Therefore, the future value that is required= $569,326.56 =539326.56+30000
This is the future value that must accumulate in the account
We have to find the annuity (each month for 35 years- from age 30 to 65) that would give us this amount
Frequency= M Monthly
No of years= 35
No of Periods= 420
Discount rate annually= 4.80% annual
Discount rate per period= 0.4000% Monthly
n= 420
r= 0.40%
FVIFA (420 periods, .4% rate ) = 1086.901432
Future value= 569,326.56
Therefore, annuity= 523.81 =569326.56/1086.901432
Answer: Mick and Moira must deposit $523.81 each month
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