Question

Question 2: You plan to retire 30 years from today on a perpetual weekly income of $1500 per week(i.e. for the purposes of this example. Assume that you live forever). Assuming that your savings earn a n APR of 5% during retirement and 7% before retirement (both with semi-annual compounding), how much money would you need to start saving at the end of each month until retirement to achieve your goal? (52 weeks in a year)

Assume that you also have $10000 dollars today to start your savings. Now what is the monthly amount you must save to attain your goals in the part above?

How much would you have to save per month in part b if you made your contributions at the beginning instead of the end of each month?

Answer 1

You need =1500*52=$78000 per year at retirement period

Effective Interest rate per year during retirement= (1+5%/2)^2-1=5.06%

Present Value i.e. Value of money required to get yearly $78000 for perpetuity= Yearly cash flow/interest rate=78000/5.06%=$1541502

Hence, at the time of retirement you need $1541502 to reach your goal

During retirement, Say, monthly equivalent interest rate is x

then (1+x)^12-1=(1+7%/2)^2-1=7.12%

or, x=0.575%

Now, interest rate=0.575%, nper=30*12=360, FV=$1541502, PMT=?

Hence, you need to save $1288.70 at the end of each month to reach your goal.

When, you $10000 to start your saving then, PV=$10000, interest rate=0.575%, nper=30*12=360, FV=$1541502, PMT=?

Hence, at this condition you need to save $1222.84 to reach your goal

If you have to save at the beginning of each month, then

You need to save $1215.85 to reach your goal.