week 7 finance

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  • Created by: jmf00632
  • Created on: 27-12-19 20:08
annuity
– a level stream of cash flows for a fixed period of time
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annuity due
an annyity for which the cash flows occur at the start of the period
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perpeturity
an annuity in which the cash flows continue for ever
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consols
– a type of perpetuity
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norminal interest rate
the interest rate expressed in terms of the interest payment made each period. also known as the stated or quoted interest rate
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• effective annual percentage rate (EAR)
The interest rate exressed as if it were compounded once a year
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annual percentage rate (APR)
The harmonized interest that expresses the total cost of borrowing or investing as a percentage interest rate
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fyi
if there is no mention of when a cash flow ocurs then it occurs at the end
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to claculate pv or fv of annuity due......
calculate pv/fv of equivalent anuity the x (1+r)
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by the way...
the annuity due has an extra year of interest
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when you get a q regarding annuity due:
e.g. find the pv of a 3 year annuity that will make a series of 100 payments at the beg of each year for the next 3 years. the rate is 10 percent.
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the first step.....
1. mae a timeline of the years ( 0 to 2)
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then........
amount / (1+r)
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last step..
and them all together
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the second approach to this formula will be...
use PV = C/r x [1 – (1/〖(1 + r)〗^t ) ]
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then....
multiply that answer by 1 + r
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find the pv of a 3 year annuity that wil make a series of 100 payments at the end of each year for the next3 years, starting with 100 at the end of year 1 and the grwonig y 6 percent a year - dis rate = 10%
use the pv growing perpetuity formula
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how do you solve for c?
state r, draw timeline and anotate it, choose app formula, sibstitue in values you, know, simplify, solve for c
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learing to solve for c will tell you....
how much you need to uild reg to build up required retirement savings, how much you can withdraw and how much you have to pay each month for finance / mor
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with the fv annuity formula...
rember to od it all sep and the do the -1 at the end
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compound periods more than once year answers..
what if interest compound was monthly, quarterly e,c,t nstead of just once a year?
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so..
we can use all formulas for pv of a single cash flow, fv of a single cash flow e.c.t.
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however we need to restate "r" and "t" to give......
interest rate per period (r) and "t" numbero f periods
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qr is
quoted rate
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M is.....
number of times the interest rate is compounded in one year
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t is....
number of periods (numbers x m)
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how to cal compudning more than once a year (1)
workou r = QR / M (TAKEN FROM EAR)
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SECOND STEP...
wokout t = number of ears x m
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what do you do when your calc fv for a single cash flow where interest compounds m times a year?
with these q it is the same formula but becuase it has been compounded quarterly to have to / i.r by how much it iss being compounded eg. quarteryl = 4
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for example - you have invested 1,000 for 5 years in a deposit account that pays annual interest of 4% comp quaeterly. wwhat is the val of your invstment after 5 years
normal single cash flow formula but you have to do r/comp amount then t (5 years) x compound amount and then use that as t (5 x 4) = 20
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how do you cal ammortised loan with fixed regular payments
if the questions asks for annual loan repayments then you use the relevant annuity formula - solving for c
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how do you solve for c
make sure you do every calc in the formula sep and then when it comes to working out c do the formula with the opp signs
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what do you do when asked how much principle and interst will be paid each year?
make a table with the headings - period year, beg balance, payment and interest
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how do you fill out that table? (payment box)
once yoube solved c by using the correct formula, you can put that figure into the payment column
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interest box
beg balcne x interest rate = 800
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principal repaid box (first one)
payment - interest (2-3)
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beg balance
beg balance - principal repaid (1-4)
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end balance
is the beg balance
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the table for loan amorisation will be different if you are asked to pay back the principal in istalements
period, beg balance, principle repaid, interest, total payment, end balance
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to calculate simple intrest.......
r x principle every period
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if asked to do fv/pv of multiple cash flows...
you do it backwards e.g 950 was in year 1 so you do that to the powr of 4 and the amount that was in year 4 you do to the power of 1 and then you add them all up
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what does compounded mean - IMPORTANT TO KNOW FOR Q
If an amount is compounded it means that it is reinvested so in the second month / second half of the year e.ct. you get interest on the first half and so on
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does the single cash flow formulas change if it is compuounded?
yes! - you do the same formula but instead of putting 1+ in brackets you put it outside of the bracket and inside you put r / the amount it is compuded e.g. 12
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if aksed for interest accured....
you do the latest amount - the amount you started with
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if mention compunding you may have to use the formul-
qr/m = r you have to remeber this! - on formula sheet but got other stuff with it
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then - for example if the amount is being compuonded monthly and they want to know how much you owe the bank after 5 years:
12 x 5 =
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if asked to calulate EAR
be careful you dont always use the equation as it has been given - you do qr / m then 1 + that answer to the power of 12 e.g. - 1
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if the q mentions cash flows - asking the fv of your investmwnt at the end
if fv - use pv - it is an annuity - find c, r, (qr/m), t - then put it in the formula
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if asked for value at the start -
find out eend (by doing above) 1 + r x previous answer
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Assuming a positive interest rate, the present value of an annuity due will always
be larger than the present value of an ordinary annuity. Each cash flow in an annuity due is received one period earlier, which means there is one period less to discount each cash flow.
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Assuming a positive interest rate, the future value of an annuity due will always
s higher than the future value of an ordinary annuity. Since each cash flow is made one period sooner, each cash flow receives one extra period of compounding.
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whats on an amorisation table? - first box and how you find it
period = months (should be in question - for example if it says semi annualy for 2 years that will be 4 periods)
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whats on an amorisatio table? - second box and how you find it
beg balance - found in q and then carried over from ending balance
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whats on an amorisation table? - 3rd box
total payment - found by doing annuity formula
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4th box
interest owed - found by doing r (which is found by doing qr/m) =r x beg alance
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5th box
principal pyment box - 3rd box - 4th box = total payment - interest owed
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6th box
eending blance - 2nd box - 5th box beg bal - principal payment
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how much interest is paid in the second year - amorisation table
you plus the second and third year interest owed (5th column)
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when asked how much interest is absorbed over the life of the loan?
add up the 5th column (interest owed)
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amorisation table - when there is an equal principal reduction every quarter
period (1), beg balance (2), total pay (3), interest payment (4), principal payment (5), end balance (6)
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so here we are solving for c
- so we start by calc the reular principal repayment - loan / r = principal repayment - thi is found by fining r, m and t
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then you can start making the table
beg balance is the number in the q, toal payment is 4+5, interst paymentn is the rate x the beg blance (2), principal payment (5) was found by doing loan / r and the end balacne is 2-5
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if the payments go on indefinetly....
it is a perpetuirity , so you use the perpeutiy formula but you do qr/ m first
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you use the single cash flow if the question only asks for....
one single cash flow
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when the question mentions compounding this is an indication / sign that you need to find
c, r, qr, t and m
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Other cards in this set

Card 2

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annuity due

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an annyity for which the cash flows occur at the start of the period

Card 3

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perpeturity

Back

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Card 4

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consols

Back

Preview of the front of card 4

Card 5

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norminal interest rate

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