Question

John, James and Joe are all 35 years old and plan to retire at age 65. They expect to live to 90

years old. Upon retirement they would all like to take immediate annual pension payments

from their savings at the start of each year. John and James can access a quoted rate of 9% per

year with quarterly compounding whilst Joe can access a quoted rate of 11% per annum with

semi-annual compounding.

a) John has a monthly income of $6,000 and monthly expenses of $2350 and saves the

remainder at the end of each month. On the day of his retirement he will receive a

retirement bonus from his employer totaling $20,000 and will also sell his holiday home

for an estimated $150,000. How much money will John have saved upon retirement?

b) What would be John’s annual pension?

c) James does not have a holiday home to sell, and will not be receiving a bonus from his

employer upon retirement. However he is able to invest twice as much as John each

month. How much later can James start saving if he wants to have the same annual

pension as John?

d) Joe also does not have a holiday home to sell, and will not be receiving a bonus from his

employer upon retirement. Unfortunately he does not believe he can save any money

during the first 5 years. However, he anticipates being able to save $6,000 per month for

the subsequent 10 years, and then $8,000 per month until retirement. Comparing Joe

with John, who has the biggest annual pension, and by how much?

use a financial calculator to solve. (BAIIplus)

effective interest rate= (1+ r/m)^m/f

make a timeline for each person.

Answer 1

Annual Effective rate = (1+r/m)^m -1

john and James can access a quoted rate of 9% with quarterly compounding = (1+9%/4)^4 -1 = 9.31 % annual

Monthly Interest rate = 9.31%/12 = 0.776%

Joe can access a quoted rate of 11% per annum with semi-annual compounding = (1+11%/2)^2 -1 = 11.303 % annual

Monthly Interest rate = 11.303%/12 = 0.942%

Answer a)

	John
Number of payment(nper)	360	(65-35)*12
Monthly saving(pmt)	3650	6000-2350
interest rate(monthly)	0.776%
Future value at retirement	$71,32,779.90	FV(0.776%,360,-3650,0,0)
Retirement Bonus	$20,000.00
Sell of home	$1,50,000.00
Total Retirement Fund	$73,02,779.90	sum of above

Answer b)

Annual Pension	$6,97,304.87
	PMT(9.31%,25,-73,02,779.90,0,1)
Number of year pension(90-65)	25
Effective rate	9.31%

Answer c)

	James
Total retirement fund	$73,02,779.90
Monthly saving	7300
interest rate(monthly)	0.776%
Total number of payment(nper)	281
	nper(0.776%,-7300,0,7302779.90,0)
Start of saving (360-281)after	79

Answer d)

	Joe
Number of payment(nper)	120	10 year
Monthly saving(pmt)	6000
interest rate(monthly)	0.942%
Future value	$13,25,192.78	FV(0.942%,120,-6000,0,0)
Value at retirement (after 15 years)	$66,04,696.26	1325192.78*(1+11%/2)^30
Number of payment(nper)	180	15 years
Monthly saving(pmt)	8000
interest rate(monthly)	0.942%
Future value at retirement	$37,42,533.34	FV(0.942%,180,-8000,0,0)
Total Retirement Fund	$1,03,47,229.61
Annual Pension	$11,28,362.80

	Joe	John	James
Annual Pension	$11,28,362.80	$6,97,304.87	$6,97,304.87

Joe have biggest pension =$11,28,362.80-$6,97,304.87= $ 4,31,057.93