Question

You are 40 years old and want to retire at age 60. Each​ year, starting one year from​ now, you will deposit an equal amount into a savings account that pays 7​% interest. The last deposit will be on your 60th birthday. On your 60th birthday you will switch the accumulated savings into a safer bank account that pays only 4.4​% interest. You will withdraw your annual income of ​$100,000 at the end of that year​ (on your 61st ​birthday) and each subsequent year until your 80th birthday. On that birthday you want to give ​$450,000 to your children. How much do you have to save each year to make this retirement plan​ happen?

Answer 1

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

PV= 100000*((1-(1+ 4.4/100)^-20)/(4.4/100))

PV = 1312138.85

Future value = present value*(1+ rate)^time

450000 = Present value*(1+0.044)^20

Present value = 190196.51

total value at age 60 = 190196.51+1312138.85

=

1502335.36

FVOrdinary Annuity = C*(((1 + i )^n -1)/i)

C = Cash flow per period

i = interest rate

n = number of payments

1502335.36= Cash Flow*(((1+ 7/100)^20-1)/(7/100))

Cash Flow = 36646.35