Question

Jose, age 25, currently saves $13500 per year in his retirement account which is expected to earn 5% return. Jose is planning to retire at 62 and needs to fund his retirement upto age, 85. He has estimated that the annual amount needed during retirement would be $47,000 in today's dollar terms. The inflation rate is expected to be 1.5%. Calculate the shortfall (if any) in his retirement account at the beginning of retirement.

Answer 1

Calculate annual amount needed at beginning of retirement
Present value (PV)	$47,000
No of payments (NPER)	37	(62-25)
Inflation rate	1.50%
Annual requirement (Future value)	Present value*(1+r)^n
Interest rate is r and number of payment is n
Annual requirement (Future value)	47000*(1.015^37)
Annual requirement (Future value)	47000*1.734777
Annual requirement (Future value)	$81,534.50
Calculate total amount that would be required in year 23 (85-62) in present value term
Real rate of return	(1+nominal rate)/(1+inflation rate) - 1
Real rate of return	(1.05/1.015)-1
Real rate of return	3.4483%
Amount required per year	$81,534.50
No of years amount required	23	(85-62)
Interest rate	3.4483%
Present value beginning of year	Annual costs + Annual costs*(1-(1+r^-n)/r)
Present value	81534.50 + 81534.50*(1-(1.034483^-22)/0.034483)
Present value	81534.50 + 81534.50*15.24415
Amount required at beginning of 23rd year	$1,324,459
Calculate the additional funding if any required
Yearly investment (PMT)	$13,500
Interest rate (Rate)	5%
No of payment (NPER)	37	(62-25)
Future value	Annual investment*((1+r^n)-1)/r)
Future value	13500*((1.05^37)-1)/0.05)
Future value	13500*101.6281
Future value	$1,371,980
There is no shortfall for retirement as the future value of current investment of $1,371,980 is higher than the amount required of $1,324,459
Thus, there is not shortfall in retirement investment