Answer:
A= $4,838.95 monthly
Explanation:
Giving the following information:
She is currently planning to retire in 30 years and wishes to withdraw $10,000/month for 20 years from her retirement account starting at that time.
First, we need to calculate the amount needed for retirement:
FV= 10,000*12*20= 2,400,000
Now, we can use the following formula:
FV= {A*[(1+i)^n-1]}/i
A= annual deposit
Isolating A:
A= (FV*i)/{[(1+i)^n]-1}
Effective rate= 0.02/12= 0.0017
n= 12*30= 360
A= (2,400,000*0.0017)/[(1.0017^360)-1]
A= $4,838.95 monthly
The amount she contribute each month for 30 years into a retirement account earning interest at the rate of 2%/year compounded monthly to meet her retirement goal is: $4,011.44
First step is to find the interest rate earned per conversion period and the total number of payment to be made.
Interest rate formula
i=r/m
Total number of payment formula
n=m×t
Substitute r=0.02, m=12 and t=20 in i=r/m and n=m×t
Hence:
i=r/m
i=0.02/12
i=0.001667
n=m×t
n=12×20
n=240
Second step is to find the principal using this formula
P= R [1-(1+i)^-n]÷i
Substitute R=10,000, i=0.001667 and n=240 in P and calculate the outstanding principal
P=[1-(1+0.001667)^-240]÷ 0.001667
P=3,295.1027680÷0.001667
P=1,976,666.3275
Third step find the interest rate earned per conversion period and the total number of payment to be made.
Interest rate formula
i=r/m
Total number of payment formula
n=m×t
Substitute r=0.02, m=12 and t=30 in i=r/m and n=m×t
Hence:
i=r/m
i=0.02/12
i=0.001667
n=m×t
n=12×30
n=360
Fourth step Substitute S=P=1,976,666.3275, i=0.001667 and n=360 in R and calculate the periodic payment
R=iS÷(1+i)^n-1
R=(0.001667) (1,976,666.3275)÷ 0.821427174
R=3,295,1027680÷0.821427174
R=$4,011.436
R=$4,011.44 (Approximately)
Inconclusion the amount she contribute each month for 30 years into a retirement account earning interest at the rate of 2%/year compounded monthly to meet her retirement goal is: $4,011.44
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