Question

You plan to retire after 30 years. After that, you need $200,000 per year for 10 years (first withdrawal at t=31). At the end of these 10 years, you will enter a reitrement home where you will stay for the rest of your life. As soon as you enter the retirement home, you will need to make a single payment of $1,000,000. You want to start saving for your retirement in an account that pays you 9% p.a. Therefore, beginning from the end of the first year (t=1), you will make equal yearly deposits into this account for 30 years. You expect to receive $500,000 at t=30 from a cash value insurance policy that you own. This money will be deposited in your retirement account. What should your yearly deposits into the account be?

Answer 1

STEP 1: amount required at age 30
Amount needed for 10 years withdrawal	$1,283,531.54
PV of payment to be made at t 41	$422,410.81
Total amount required at Year 30	$1,705,942.35
STEP 2: Amount required in form of deposits
Insurance policy amount at year 30	500000
Balance amount to be raised by deposits	$1,205,942.35
STEP 3: Deposit amount
Annual deposits required	$8,847.22

WORKINGS