math chapter 13 ravi Flashcards
what is J?
the anual interest rate (also called nominal rate) NOM%
what is J on the calculator?
NOM%
what is N
time period
what is PV
present value (amount of money today)
what is PMT
payment
what is FV
Final Value (amount of money at the end)
p/yr?
compounding periods per year
how do you set up your calculator to one decimal point
- red down key
- = sign
- decimal sign
on calculator, if you press..
red arrow down/decimal/3
what happens?
it will go 3 decimal points (numbers)
how would you push 13% into the calculator
- 13
- red arrow down (this means second function)
- NOM (wich is on the i/yr button)
how would you put in
payment of $250
vs
receiving $250
payment
- 250
- (press the +/- button)
- PMT
receiving
- 250
- PMT
what does p/yr mean
compounding periods per year
how would you enter daily/weekly/monthly/quarterly in compounding periods per year on the calculator?
365 down arrow (second function) PMT(second function = p/yr)
52
down arrow
p/yr
etc
how to clear the calculator including memory from previous question
- red down arrow
2. C (clear)
whaat does RCL mean on the calculator
it means recall, so for example, you can press RCL and then N and see the time period for the previous calculation
after doing the compounding periods/year and the interest rate
what is the order you should do on the calculation
go from left to right
so start with the N (period of time) and move towards FV
How do you calculate per annum?
Divide the annual interest amount by 12 to calculate the amount of your per annum interest payment that is due each month. If you owe $600 for the year, you make monthly payments of $50. Another way to make the same calculation is to divide the annual interest rate by 12 to calculate the monthly rate.
anytime money is going out of your pocket you must put it as _____ in the calculator?
negative (-)
on an interest accruing loan how much money do you pay per month
$0
difference between interest only loan and interest acruing loan?
interest only, means every coupounding period you are paying the interest rate back to the lender
with interest accruing, the borower does not pay the interest back until the final payment when he/she pays back the principal
accruing loan is for 8 months
if it is J12
and N = 8 months
what is the P/YR?
12!! dont be confused by the 8 months
-Get a loan of $300,000
-and getting a further loan of 2,000 per month
-how much to return after 5 years
j12= 10%
J12 = 10% N = 5 years (60 months)
PV————-pmt————FV
$300,000–2,000———?
FV = - $648,466.82
Minus means to be given to lender after 5 years answer the question will be 493,592.68 will need to be returned
Get a loan of $300,000
How much to return after 5 years
J12 = 10%
N = 5 years (60 months)
J12 = 10% N = 5 years (60 months)
PV——————-pmt—————FV
$300,000———0——————-?
FV = - $493,592.68
Minus means to be given to lender after 5 years answer the question will be 493,592.68 will need to be returned
-Get a loan of $300,000
-making a payment of 2,000 per month
-how much to return after 5 years
J12 = 10%
J12 = 10% N = 5 years (60 months)
PV——————-pmt———–FV
$300,000——–(-2,000)——-?
FV = - $338,718.54
Minus means to be given to lender after 5 years answer the question will be 338,718.54 will need to be returned
How long to double your money with 100k deposited @
J12 = 10%
N = ?
PV—————— FV
- 100,000 $200,000
(deposited) get
N = 83.52 months
Approximately 7 years
Interest only loan
For an interest only loan money borrowed is the same amount as money to be returned
That means pv and fv are the same amount but the opposite signs
j1= 10 N = 5
pv———pmt——fv
$+50,000—?——$-50,000
$-5,000 per year
All payments the same
Last payment $5,000 plus 50,000(principal that has to be returned = 55,000
Interest only loan
50k deposite
j2= 9% N = 5 (5 X 2 = 10)
how much will be paid per period???
j2= 9% N = 5 (5 X 2 = 10)
pv ———pmt ———–fv
$+50,000—?——–($-50,000)
$-2,250 per 6 months (semi annual) last payment 2,250 plus 50,000 = 52,250
Interest only loan starts june 01, 1990
50k loan amount
j4= 8% N = 5 (5 X 4 = 20 quarters)
what are the quarterly payments??
what is the second payment?
what is the last payment?
when is the last payment?
pv —— pmt——–fv
$+50,000–?——($-50,000)
$-1,000 per quarter (every 3 months)
All payments are the same
How many payments = 20
What is the second payment: $1,000
What is the last payment $1,000 plus $50,000 = $51,000
When is the last payment : may 31, 1995
Interest accruing loan
No payment during the loan (PMT - $0 per month)
50k loan
j12= 10% N = 5 (5 X 12 = 60 months)
pv —— pmt——–fv
$+50,000–?——($-50,000)
No payment during the loan
FV = -63,814.08
Final amount total accrued is $63,814. 08
Interest accruing loan
J4 = 10%
N = 5 years (20 quarters)
50k loan
pv —— pmt——–fv
$+50,000–0——?
No payments
The final total accrued is $81,930.82
Owing 81,930.82 after 5 years
Interest accruing loan starting sept 01, 2021 for 8 months
J12 = 10%
N =8 months
50k loan
pv —— pmt——–fv
$+50,000–0——?
No payments during the term
Final total accrued is $-53,432.19
Owing 53,432.19 after 8 months
This one is tricky for p/yr don’t let the 8 month trick you, the compound is right beside the J (12)
Buy a car?
Car value = $25,000
Saving put in (bank) now $-10,000
Saving per year = 0
J1 = 10%
N =?
pv —— pmt——–fv
$-10,000–0——$25,000
N= 9.6 years
You are offered an investment that will produce $250,000 in 5 years. If you wish to earn 4% per annum compounded monthly, how much should you offer to pay for the investment today rounded to the nearest $10
J12 = 4%
N =8 months
a. $212,250
b. $204,750
c. $221,140
d. $231,120
pv —— pmt——–fv
?————-0——$250,000
b. $204,750 is correct answer
Buy a car?
Car value = $25,000
Saving put in (bank) now $-15,000
Saving per year = 0
J1 = 10%
N =?
pv —— pmt——–fv
$-15,000——0——$25,000
N= 5.35 years
Buy a car?
Car value = $25,000
Saving put in (bank) now $-15,000
Saving per year = 0
J1 = 2%
N =5 years
will you have enough money in the bank account after 5 years to buy the car?
pv —— pmt——–fv
$-15,000——0——?
$16,561. 21
Will have $16,561.21 in 5 year in the bank account to buy the car
Will NOT have enough money to buy the car
Short by $25,000 - $16,561.21 = $8,438.79
When it says - savings per year = 0 (this means NO PMT’s per year)
PVT = saving today PMT = 0 saving per year Loan = 50,000
J1 = 10% N = 5 years
pv —— pmt——–fv
$50,000——0——?
-80,525.50
1 (compounding period/see where it says J1) then red down arrow (Second function) then P/YR (PAYMENT BUTTON)
Interest rate next which is… 10 red arrow down NOM%
5 then N (TIME)
50,000 (PV) present value
0 (PMT)
Next press FV and you get -80,525.50
If you invest $200,000 today at an interest rate of 4% per annum, compounded annually, what is the value of this investment after 5 years rounded to the nearest $10?
a. $234,639.58
b. $234,720.58
c. $243,330.58
d. $246,230.58
J1 = 4% N = 5
pv —— pmt——–fv
$200,000——0——?
answer is C. $243,330.58
Interest rate = 1 (red arrow down) P/YR 4 / I/YR 5(N) - time 200,000 (PV) 0 (PMT) Then press FV
=$-243,330.00 (dont worry about the negative at this time)
If you invest $200,000 today at an interest rate of 4% per annum, compounded semi-annually, what is the value of this investment after 5 years(60 months) rounded to the nearest $10?
Think number of birthday parties for N
a. $246,230.58
b. $234,720.58
c. $351,639.58
d. $243,800
J2(semi annually!!) = 4%
N = 5 X 2 = 10 semi annual periods
Note- they pointed out 60 months just to confuse you!!!
pv —— pmt——–fv
$200,000——0——?
answer = D. $243,800
2 compounding periods (red arrow down) P/YR 4 (4%)/ I/YR 10(N) - time 5 X 2(semi annually) 200,000 (PV) 0 (PMT) Then press FV
=$-243,330.00 (dont worry about the negative at this time)
Saving at the start $50,000
Also $10,000 saving per month
J12(monthly!!) = 10% N = 5(5 X 12 = 60 months)
pv —— pmt——–fv
$50,000—$10,000per month——?
FV = - $856,636.16
J12(monthly!!) = 10%
N = 5(5 X 12 = 60 months)
100k saved up to be deposited
going to pay $1000 per month back to the bank
pv —— pmt——–fv
$-100,000—$-1,000per month——?
(saved up) (pay bank)
FV = $241,967.96
12 (RED) P/YEAR 10 (RED) NOM 60 N -100,000 PV -1000 PMT
buy a car = $25,000
saving put in bank now (-15,000)
saving per year = 0
j1= 2% N = 5 years
will you have enough to buy the car in 5 years?
___________________________________
pv pmt FV
$-15,000 0 ?
$16,561.21
will have $16,561.21 in 5 years to buy the car
will not have enough money to buy the car as he is short
$25,000 - $16,561.21 = 8,438.79
tricky part on this one is that it gives the $25,000 value but we don’t use it in the calculation anywhere but to see if he has enough money
buy a car?
car value = $25,000
saving put in bank now $-10,000
saving per year ?
j1 = 10% N = 5 year
________________________________________
pv pmt ? FV
$-10,000 ? $25,000
= $1,456.96 per year
save $1,456.96 per year to buy the car in 5 years
super easy, but i put -25,000 when it should have been 25,000. i think we have to remember 25,000 is the future amount, not the amount that we are paying out of the pocket but the amount that that the payments need to result in to get to $25,000