Question

Your 21 year old client just graduated from college and started a job with monthly salary of $5,000 per month. He wants to retire when he is 60 years old and wants to start saving for retirement right away. We cannot be sure of how long we live after retirement, but the client wants to be extra careful and save for 30 years of after retirement life. Market expectation for average annual inflation for the future is 1.7% (Let’s assume inflation to be 0 after retirement period). Because of inflation, he will need substantially higher retirement monthly income to maintain the same purchasing power. He plans to purchase a lifetime annuity from an insurance company one month before he retires, where the retirement annuity will begin in exactly 39 years (468 months). The insurance company will add a 2.00 percent premium to the pure premium cost of the purchase price of the annuity. The pure premium is an actuarial cost of his anticipated lifetime annuity. He has just learned the concept of time value of money and never saved anything earlier. He will make the first payment in a month from now and the last payment one month before he retires (a total of 467 monthly payments).

1) Given a rate of return of 4% for the foreseeable future, how much does he need to save each month until the month before he retires?

Answer 1

Present equivalent (monthly) of retirement income required in 39 years (468 months) (A)		$5,000
Annual rate of inflation (i)		1.7%
Therefore, monthly income required after retirement in 39 years in order to have the same purchasing power	=A*(1+i)^39	=$5,000*(1+0.0175)^39 =$5,000* 1.967172 =$ 9835.86
Since inflation post retirement is assumed to be 0, this requirement is treated as constant
Annuity amount for earning income as above, for 30 years (360 months) Discount rate 4%	Calculated in Excel , details below as screen shot	$2,060,231.44

Annuity amount for earning income as above, for 30 years (360 months)	As above	$2,060,231.44
Add: 2% premium by insurance company	$2060231.44*2%	$41204.63
Purchase price of annuity	$2,060,231.44 + $ 41204.63	$2,101,436.07
Monthly payments required for the above amount, for 467 months. Interest rate 4%	Calculated in Excel , details below as screen shot	$1877.60