Question

you are 25 years old who want to determine how many $ to deposit today in the bank that pays 5% compounded contineously so that when you reaches 60years old you can withdraw 1000 $/month until you reach 80 years old ,Also draw the cash flow diagram

Answer 1

In this case, the person will invest lump-sum amount at age of 25 years. This amount will remain invested for 35 years compounding annually at 5%. At age of 60 years - Maturity amount will be converted into annuity for 20 years with monthly pay out of $1000.

First we need to calculated the Maturity amount required at age of 60. This can be calculated by discounting monthly cash flows.

Monthly Rate of interest = 5/12=0.4167%

Number of Period =240

Cash Flow at end of each period =$1000

Using PV (Present Value Function) we can find - PV = (Rate,nper,pmt,FV,type)

PV = $151,525.31 -

Hence, Person will need $151,525.31 at end of 60 years.

Rate of Interest = 5%

Years = 35 Year

FV= Maturity Value = $151,525.31

Using PV ( Present Value function) we can find PV = (Rate,nper,pmt,FV,type)

Initial investment should be $ 27,470.07.

Cash flow attached below -

Age	Months	Cash Flow
25	0	$             -27,470.07
60	1	$                 1,000.00
60	2	$                 1,000.00
60	3	$                 1,000.00
60	4	$                 1,000.00
60	5	$                 1,000.00
60	6	$                 1,000.00
60	7	$                 1,000.00
60	8	$                 1,000.00
60	9	$                 1,000.00
60	10	$                 1,000.00
60	11	$                 1,000.00
61	0	$                 1,000.00
61	1	$                 1,000.00
61	2	$                 1,000.00
61	3	$                 1,000.00
-	-	-
-	-	-
-	-	-
79	8	$                 1,000.00
79	9	$                 1,000.00
79	10	$                 1,000.00
79	11	$                 1,000.00
80	0	$                 1,000.00