+598 Mrs. Bell expects to retire in 7 years and would like to receive $ 800 at the end of each month for 10 years following the date of her retirement. How much must Mrs. Bell deposit today in an account paying 7.5% compounded semi- annually to receive the monthly payments?
Any help with steps would be greatly appreciated. Thanks
Mrs. Bell expects to retire in 7 years and would like to receive $ 800 at the end of each month for 10 years following the date of her retirement. How much must Mrs. Bell deposit today in an account paying 7.5% compounded semi- annually to receive the monthly payments?
Any help with steps would be greatly appreciated. Thanks
Mrs. Bell must deposit today $40,456.61. We project this amount 7 years into the future and we get
$67,736.54. This will enable Mrs. Bell to withdraw $800 per month every month for 10 years.
This is a bit tricky to calculate. First, you have to find the PV of 120 payments of $800 each, which comes to $67,736.54. But, this amount is 7 years in the future. So, you have to find its PV today:
Here are the two formulae you need to do this:
PV=P{[1 + R]^N - 1.[1 + R]^-N} R^-1=PV OF $1 PER PERIOD...........(1)
Once you found that, then you set it as FV and find its PV according to this common formula:
PV=FV[1 + R]^-N=PV OF $1 IN THE FUTURE....................................(2)
Where R=Interest rate per period, N=number of periods, P=periodic payment.
PV=Present value, FV=Future value.
