Question

On your 30th birthday your employer SWFC Corporation, has invited you to join their pension scheme. You are paid $60,000 per year, and at the end of each year the company contributes an additional 10% of your salary to the scheme.

How much money will be in your fund at age 60 (your projected retirement age), if the fund expects to earn an average rate of 11% p.a.?

After retiring at age 60, you want to use your cash payout (from answer i) to buy a monthly annuity payable at the end of each month. The fund will invest your money safely and so will earn a relatively low expected rate of return, namely 6% APR compounded monthly. Statistics project that you will live until age 85. How much can you expect to receive as your monthly pension (payable at the end of each month)?

Answer 1

Hi

Annual contribution from company C = $60000*10% = $6000

time t = 60-30 = 30 years

rate r = 11%

Future Value at age 60= (C/r)*((1+r)^t -1 )

= (6000/0.11)*(1.11^30 -1)

=54545.45*21.89

=$1,194,125.27

Now For the second part of question

Present Value PV at age 60 = $1,194,125.27

monthly rate r = 6%/12 = 0.5%

time t = 85-60 = 25 years = 300 months

Monthly Pension C=?

PV = (C/r)*(1-(1+r)^-t)

1,194,125.27 = (C/0.005)*(1-1.005^-300)

C = 1194125.27*0.005/0.776

C = $7,693.77

Hence each month you will receive $7,693.77

Thanks