# week 7 finance

0.0 / 5

- Created by: jmf00632
- Created on: 27-12-19 20:08

annuity

– a level stream of cash flows for a fixed period of time

1 of 65

annuity due

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

2 of 65

perpeturity

an annuity in which the cash flows continue for ever

3 of 65

consols

– a type of perpetuity

4 of 65

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

5 of 65

• effective annual percentage rate (EAR)

The interest rate exressed as if it were compounded once a year

6 of 65

annual percentage rate (APR)

The harmonized interest that expresses the total cost of borrowing or investing as a percentage interest rate

7 of 65

fyi

if there is no mention of when a cash flow ocurs then it occurs at the end

8 of 65

to claculate pv or fv of annuity due......

calculate pv/fv of equivalent anuity the x (1+r)

9 of 65

by the way...

the annuity due has an extra year of interest

10 of 65

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.

11 of 65

the first step.....

1. mae a timeline of the years ( 0 to 2)

12 of 65

then........

amount / (1+r)

13 of 65

last step..

and them all together

14 of 65

the second approach to this formula will be...

use PV = C/r x [1 – (1/〖(1 + r)〗^t ) ]

15 of 65

then....

multiply that answer by 1 + r

16 of 65

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

17 of 65

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

18 of 65

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

19 of 65

with the fv annuity formula...

rember to od it all sep and the do the -1 at the end

20 of 65

compound periods more than once year answers..

what if interest compound was monthly, quarterly e,c,t nstead of just once a year?

21 of 65

so..

we can use all formulas for pv of a single cash flow, fv of a single cash flow e.c.t.

22 of 65

however we need to restate "r" and "t" to give......

interest rate per period (r) and "t" numbero f periods

23 of 65

qr is

quoted rate

24 of 65

M is.....

number of times the interest rate is compounded in one year

25 of 65

t is....

number of periods (numbers x m)

26 of 65

how to cal compudning more than once a year (1)

workou r = QR / M (TAKEN FROM EAR)

27 of 65

SECOND STEP...

wokout t = number of ears x m

28 of 65

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

29 of 65

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

30 of 65

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

31 of 65

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

32 of 65

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

33 of 65

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

34 of 65

interest box

beg balcne x interest rate = 800

35 of 65

principal repaid box (first one)

payment - interest (2-3)

36 of 65

beg balance

beg balance - principal repaid (1-4)

37 of 65

end balance

is the beg balance

38 of 65

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

39 of 65

to calculate simple intrest.......

r x principle every period

40 of 65

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

41 of 65

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

42 of 65

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

43 of 65

if aksed for interest accured....

you do the latest amount - the amount you started with

44 of 65

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

45 of 65

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 =

46 of 65

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

47 of 65

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

48 of 65

if asked for value at the start -

find out eend (by doing above) 1 + r x previous answer

49 of 65

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.

50 of 65

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.

51 of 65

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)

52 of 65

whats on an amorisatio table? - second box and how you find it

beg balance - found in q and then carried over from ending balance

53 of 65

whats on an amorisation table? - 3rd box

total payment - found by doing annuity formula

54 of 65

4th box

interest owed - found by doing r (which is found by doing qr/m) =r x beg alance

55 of 65

5th box

principal pyment box - 3rd box - 4th box = total payment - interest owed

56 of 65

6th box

eending blance - 2nd box - 5th box beg bal - principal payment

57 of 65

how much interest is paid in the second year - amorisation table

you plus the second and third year interest owed (5th column)

58 of 65

when asked how much interest is absorbed over the life of the loan?

add up the 5th column (interest owed)

59 of 65

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)

60 of 65

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

61 of 65

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

62 of 65

if the payments go on indefinetly....

it is a perpetuirity , so you use the perpeutiy formula but you do qr/ m first

63 of 65

you use the single cash flow if the question only asks for....

one single cash flow

64 of 65

when the question mentions compounding this is an indication / sign that you need to find

c, r, qr, t and m

65 of 65

## Other cards in this set

### Card 2

#### Front

annuity due

#### Back

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

### Card 3

#### Front

perpeturity

#### Back

### Card 4

#### Front

consols

#### Back

### Card 5

#### Front

norminal interest rate

#### Back

## Similar Business Management resources:

0.0 / 5

0.0 / 5

0.0 / 5

0.0 / 5

0.0 / 5

0.0 / 5

0.0 / 5

0.0 / 5

0.0 / 5

0.0 / 5

## Comments

No comments have yet been made