00:22the next segment we're going to discuss
00:24our annuities annuities are a set
00:29payment for a set period of time two
00:31good examples of annuities are mortgages
00:33and retirement plans a mortgage you have
00:38a set payment each month you continue to
00:40pay it until the mortgage is paid off
00:41we'll take a look at how to calculate
00:43that retirement we actually use two
00:46sides to the annuity where you make a
00:48set payment going into your retirement
00:50plan for a set period of time and then
00:52you make withdrawals fresh that period
00:54of time with those payments coming to
00:55you let's take a look at annuities what
00:59is an annuity an annuity is a level
01:03stream of cash flows for a fixed or a
01:06certain period of time at regular
01:09intervals so when we look at annuities
01:14we're looking at the stream of cash
01:16flows that could be coming to us or
01:18could be outflows number negatives
01:20versus positives and that would become
01:24our payment so the future value of an
01:30annuity think of the future value of an
01:33annuity as the sum of all those future
01:36values of each individual cash flow in
01:40reality we could put each cash flow into
01:43a separate account let it accumulate its
01:46interest and then put them all together
01:48and we would have the same future value
01:59so if we took $100 per year for three
02:02years with the first deposit being made
02:06a year from now or at the end of the
02:08first year earning 7% per year how much
02:14would you have in the account after you
02:15made that last deposit let's take a look
02:18at our timeline I've got three payments
02:23there at the end of each year and at the
02:27end of the third year is when I'm going
02:30to take the money out so I put that $100
02:34in my third payment at the end of the
02:36third year that is worth $100 at the end
02:44of the second year I put in $100 at 7%
02:48that was there for one year see that
02:52from year to two year three it earned
02:56its $7 so it's worth a hundred and seven
03:03the first deposit I made had two years
03:08worth of interest it compounded and had
03:12is worth one hundred and fourteen
03:15dollars and 49 cents so the future value
03:19of that one annuity is three hundred and
03:24twenty one dollars and forty nine cents
03:27put another way if I deposit $100 per
03:30year for the next three years at seven
03:32percent I will end up with three hundred
03:35and twenty one dollars and forty nine
03:37cents now that was a pretty difficult
03:42way to do that wasn't it let's use the
03:45calculator remember do not you should
03:51not see b/g/n at the top of your
04:07the numbers we're dealing with we have
04:10three periods interest rate is 7% per
04:13year my payment this is the money I'm
04:18putting into the annuity is $100 I'm
04:22putting it in that's a negative cashflow
04:23and we want to see what it ends up
04:25amounting to present value is zero we're
04:28starting with nothing so go ahead and
04:32clear a calculator I have three in my
04:41interest rate was seven percent per year
04:43I'm starting with zero I am adding a
04:49payment of $100 each period I can
04:56compute my future value three hundred
05:02and twenty one dollars and forty nine
05:03cents was exactly what we came up with
05:05when we looked at each one of the
05:06individual future values let's look at
05:14another annuity this is one we can all
05:18relate to in order to accumulate
05:23$100,000 in the college fund by age 18
05:27what is the annual payment that must be
05:30invested if your investment yields 8%
05:34hopefully mom and dad started this on
05:36your first birthday so where will be on
05:38track if they didn't do it maybe you can
05:42use this problem to try and save
05:45$100,000 for your children we have 18
05:50years we have 8% interest rate per year
05:56and we know we want the future value to
05:59be $100,000 we're starting with nothing
06:02so how much do we need to pay each year
06:05to reach that $100,000 let's use our
06:11calculator clear time value of money
06:13erase the numbers I have 18 years or 18
06:20I have an 8% interest rate per period I
06:25have a zero start and I have $100,000
06:32that I want to come back to me in the
06:36future do we want to see the payment two
06:45thousand six hundred seventy dollars and
06:4721 cents so if mom and dad deposited two
06:51thousand six hundred seventy dollars per
06:53year for you starting on your first
06:55birthday by the time you're 18 and they
06:58and they earned a yield of eight percent
07:00they'll have one hundred thousand
07:02dollars for your college fund
07:13let's think about this if those payments
07:16were made monthly instead of paying two
07:19thousand six hundred seventy dollars
07:20each month or each year could they make
07:23an equal payment divided twelve equal
07:27payments or would it be something
07:30different there's how we would solve
07:35that in 18 years we would have two
07:40hundred and sixteen months that eight
07:46percent divided by twelve would give us
07:48point six six so let's take a look at
07:53the calculator again clear my time value
07:56of money so I have 18 since most of us
08:02aren't that good at math let's check
08:03that 216 I have 18 years times 12 months
08:09equals 216 periods we had 8% interest
08:19divided by 12 equals 0.666 repeating
08:25will be my interest rate I had a zero
08:31payment or backed-up sorry I had a zero
08:35present value and we have a $100,000
08:45let's compute the payment payment is 208
09:01if we take the two thousand six hundred
09:04seventy dollars in 21 cents of our
09:06annual payment divided by twelve that'd
09:08be a a monthly payment of two hundred
09:10and twenty-two dollars why is the two
09:14hundred and eight less than two twenty
09:17two well the reason is the compounding
09:24because we compounded that two hundred
09:27and eight dollars every month we added
09:30an extra two hundred and eight dollars
09:31and we're able to get interest on each
09:34one of those monthly payments over the
09:36course of the year over eighteen years
09:38we actually saved a considerable amount
09:46let's look at the present value of an
09:50annuity using a ten percent discount
09:55rate what is the present value of one
10:01hundred dollars to be received at the
10:02end of each of the next three years
10:10so if we looked at the present value of
10:13each one of those we can calculate those
10:16on the calculator we would have each one
10:24of those present values and needing to
10:26deposit two hundred and forty eight
10:27dollars and sixty-eight cents notice how
10:35each one of those values decrease
10:45first president value is 90 then 82 then
10:4875 because the $75 will be there for a
10:54longer period of time before we actually
10:56draw that out so we deposit two hundred
11:01and forty eight dollars and sixty eight
11:03cents we can withdraw $100 each year so
11:12the present value of an annuity equals
11:14the sum of those present values of each
11:17payment so again those present values
11:20are additive let's go ahead and solve
11:26one what is the present value of $1,000
11:31to be received at the end of each year
11:34for the next five years before we do the
11:39calculator let's take a look at each
11:42year individually the first year to get
11:47$1,000 I would have to deposit 934
11:51dollars and 58 cents present value of
11:56that $1,000 is 934 dollars year to the
12:03present value of $1000 two years from
12:06now is 873 and we can do this for each
12:10of the five years add those together we
12:16have four thousand one hundred dollars
12:18and 20 cents so what is this telling me
12:23if I deposit four thousand one hundred
12:27dollars and 20 cents for the next five
12:30yet seven percent for the next five
12:32years I can withdraw one thousand
12:36dollars now that's the long way it's a
12:41whole lot easier if we do this on the
12:48five years at 7% per year at the end of
12:54the five years I have no future value
12:56left and my payment is a foul is $1,000
13:00and notice that's a positive number the
13:04$1,000 is coming to me each month that's
13:09the present value will be the outflow
13:12that I put into an account to draw that
13:16$1,000 so we clear our calculators I
13:26I have 7% each period my payment is
13:33coming to me I have a zero future value
13:37compute my present value 4100 in
13:42nineteen 4100 dollars and twenty cents
13:46the same thing we amount we came up with
13:49doing it the long way
14:07now we've solved for everything except
14:12the payment amount here so if you borrow
14:16so let's solve payment solved for a
14:18payment on a house payment if you borrow
14:21money to buy a house the payment
14:24required to pay off that loan represents
14:25an annuity it's a regular payment at
14:28regular intervals the loan amount that
14:31you borrow is the present value at the
14:35end of that mortgage you should have a
14:39zero balance which would be your future
14:41value so the annuity payments include
14:45interest that you would have to pay on
14:47the unpaid balance each month and some
14:50of the amount would go to Brutus the
14:51principal of the loan so let's take a
14:58look at a $100,000 house that we have an
15:14so if we're making monthly payments can
15:18we assume that we're going to be dealing
15:19with months in terms of interest and
15:21timeframe so let's take a look at the
15:26calculator clear my time value of money
15:30I have 30 years times 12 months I have
15:38360 periods I had nine percent interest
15:43but I want to make that a month late
15:45nine divided by 12 equals 0.75 the loan
15:53that came to me was $100,000 is my
15:58present value at the end of the mortgage
16:01I will have a future value of zero
16:05compute my payment I need to make
16:09payments each month of 804 dollars and
16:20so now I've calculated the payment
16:30if we went ahead and borrowed $100,000
16:33at 10% and you made annual payments how
16:37long would it take you to pay it off so
16:40we have four factors and we're going to
16:44solve for the number of periods
16:54their time value of money I have 10
16:59percent per year I have that loan of
17:04$100,000 is my present value I decided
17:08to make payments of $12,000 each year
17:12because I'm making that payment it's an
17:14outflow or a negative number
17:16my future value is 0 how long will that
17:21take me compute in 18 point 8 years
17:26how long is 18 point 8 years just under
17:3519 years so the last payment will be a
17:38little bit less than $12,000 now we've
17:46talked about doing monthly compounding
17:48would it be easier to take that $12,000
17:53and make monthly payments so if I make a
17:57monthly payment of $1,000 will I pay it
18:09so we'll put those numbers into the
18:16clear my time value of money my interest
18:34so I take 10/12 put my interest rate in
18:41I had a $100,000 present value
18:53my payment is 1,000 and my future value
19:00is zero compute for n I get two hundred
19:08and fifteen point nine one months how
19:13long is two hundred and fifteen point
19:23/ 12 equals seventeen point nine nine
19:28years or almost eighteen years when I
19:34did twelve thousand dollars per year it
19:39took almost 19 years now I'll be
19:45completed in two hundred sixteen months
19:47or eighteen just under eighteen years so
19:54why why does it pay off faster because
20:01each month I'm lowering the principal
20:04sum charged less interest now let's take
20:11a look the last problem I want to walk
20:14you through is a multiple step
20:17retirement problem let's go ahead and
20:20plan for our retirement
20:25this will take a couple of steps you
20:29plan to retire at age 65 and you want
20:32$2,000 per month until age 85 so it'd be
20:36a 20 year time frame you're currently 25
20:39years old and can earn a 6% annual and
20:41you will return how much should we start
20:44saving now notice I put the timeline
20:47here for you going from age 25 out to
20:50age 85 but we have something happening
20:53at age 65 we're gonna split this problem
20:56into two pieces we're first going to
21:00solve this piece at the end I want
21:03$2,000 per month how much do I have to
21:06start with that would be in this piece
21:09of the timeline the earlier part point
21:14on the timeline is the present value the
21:15later point is the future value in
21:17between are the payments then we'll look
21:21at how we get to this present value so
21:25let's first find the present value of
21:27the annuity we need at age 65 to provide
21:38we have 20 years or 240 months at 6% or
21:461/2 percent per month so we'll put those
21:51numbers into the calculator clear my
21:54time value of money so my 20 years I
22:03have 12 months times 20 years equals 240
22:09I had 6% divided by 12 used to be a
22:16point 5 I want that payment coming to me
22:20of $2,000 and I need zero money left
22:26over at the end compute my present value
22:30so at age 65 I need the two hundred and
22:38seventy nine thousand dollars in order
22:42to provide me with two thousand dollars
22:43a month for those 20 years so we now
22:47know the present value of the annuity
22:49how do we get to that number
22:55this future value or what was our
22:59present value will become our future
23:02value on the second part of the timeline
23:04we now have 40 years at 1/2 a percent
23:14and we're going to compute the payment
23:22clearer time value of money
23:39so I have 40 years to save times 12
23:45months each years 480 periods I still
23:48have I'm sorry 6% divided by 12 months
23:56equals 1/2 of 1% I'm starting with
24:00nothing and I need a future value they
24:05remember that number 279 one six one
24:10point five four that's my future value
24:20I can now compute my payment over 40
24:26years from age 25 to 65 if I make a
24:31payment of one hundred and forty dollars
24:33an annual interest rate of 6% I will
24:37have my future value of two hundred and
24:40seventy nine thousand dollars so my
24:44payment is one hundred forty dollars and
24:50during this phase I pay one hundred
24:54forty dollars each month reach a lump
24:57sum here of two hundred seventy nine
24:59thousand one hundred sixty one dollars
25:01that will provide me as long as I keep
25:04earning 6% interest with two thousand
25:06dollars each month it's your age 85
25:22so two steps we have 480 months in this
25:27piece 240 months here my payment works
25:31out to 140 going out each month and in
25:36the end with 2000 coming back to me each
25:46there's my 1:40 and there's my mm in the
25:50second in during the retirement phase
25:54this $279,000 was a present value on the
25:58first piece and the future value on the
26:00second half so as you can see by saving
26:09$140 a month for 40 years you can
26:14actually be paid $2,000 a month for 20
26:19years you could use a prop a problem
26:24similar to this in your retire in your
26:26personal financial plan if you were to
26:30set up a retirement goal remember we
26:33talked about goals in one of the earlier
26:34segments if I set up a goal of $2,000 a
26:37month in retirement right here I have
26:41the numbers that I can use to achieve
26:45that goal we've just talked about
26:48annuities now you're able to do your
26:53retirement plan you'll be able to come
26:55up with a monthly amount that you want
26:57to put into a retirement plan in order
26:59to develop a lump sum that you can use
27:02to withdraw from having another annuity
27:05coming to you we also took a look at
27:07mortgages where you're making those
27:10regular payments to pay off your
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