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
buy a car?
car value = $25,000
saving put in bank now $-10,000
saving per month?
j12 = 10% N = 5 year (60 months)
________________________________________
pv pmt FV
$-10,000 ? $25,000
PMT = 110.37 per month
save $110.37 per month to buy car after 5 years
buy a car?
car value = $25,000
saving put in bank now $-10,000
saving per year = 0
j1 = ? N = 5 year
______________________________
pv pmt FV
$-10,000 0 $25,000
j1 = 20.11%
deposit $10,000 today at 20.11
after 5 years there will be $25,000 in the bank account to buy the car
time to buy a car?
car value = $25,000
saving put in bank now $-10,000
saving per month = 0
j12 = ? N = 5 year(60 months)
_____________________________
pv pmt FV
$-10,000 0 $25,000
j12 = 18.47 %
this is annual interest rate with monthly compounding at j12 = 18.46 there will be $25,000 dollars in the account if you start with $10,000
Time to buy a car?
car value = $25,000
saving put in bank now $-10,000
saving per month = 0
j12 = ? N = 5 year(60 months)
____________________________
pv pmt FV
$-10,000 0 $25,000
NOTE, WHEN LOOKING FOR INTEREST RATES, PRESSING THE SECOND FUNCTION (RED ARROW DOWN) DOESNT WORK ON THE CALCULATOR*
J12= 18.47%
this is the annual intreat rate with monthly compounding at j12 = 18.46% there will be 25,000 dollars in the account if you start with 10,000
Joe wants to buy an investment home and wants to hold it for 15 years. he wants to earn 7% interest per annum
compounded annually. what is the maximum price he should pay for the home if it will sell for 1,000,000 in 15 years?
a. $413,913.25
b. $513,913.25
c. $362,446.02
d. $313,913.25
j1=7%
N = 15
_______________________________________
PV PMT FV? ? 1,000,000
a. $413,913.25
b. $513,913.25
c. $362,446.02
d. $313,913.25
answer = C $362,446.02
mistake i made, need to put (0) for the payment, and then you are looking for the PV at the end which i mixed up with PMT’s!!! Notice that the question was asking “what is the PRICE he should pay for the home”, not “WHAT ARE THE PAYMENTS”
jane got an interest only loan in the amount of $300,000. the interest rate charged on the loan is 5% per annum, compounded semi annually with semi annual payments. if the term of the loan is 2 years, what amount will be due every 6 months and as the last payment after 2 years.
a. 7,500, 307,500
b. 2,000 , 202,000
c. 2,500 , 201,000
d. 2,300 , 200,000
j2=5%
N=2
_____________________________
PV PMT FV
$300,000 ? $-300,000
tricky part on this one, i didn’t know to put -300,000 as the future value! i had it as 0, keep in mind the money has to
be paid back so it will be a negative (-) out of pocket.
a. 7,500, 307,500
is the answer. payment of $7,500 every 6 months last payment is 300,000 + 7,500 = $307,500
an interest accruing loan of $250,000 was started with a term of 8 years and an interest rate of 4.5 per annum,
compounded monthly. calculate the amount that will accumulate at the end of 8 years.
a. $335,048.92
b. 435,048.92
c. 535,048.92
d. $358,091.16
12=4.5%
N = 8 (8 X 12 = 96)
_____________________________
PV PMT FV
250,000 0
answer = D $358.091.16
what is the monthly, quarterly or yearly payment on an accruing loan?
0
john got $350 from his mom as a gift. he wants to use the money in 3 years to pay $1,000 for a helmet. john has deposited the money in a savings account bearing a periodic interest rate of .5% per month (j12 = (.5% * 12) = 6%. will john have enough money to pay for the helmet in 3 years? if he will not have enough money how
long will it take john to have $1,000
a. $435 short, 140 months
b. $581.17 short, 210.49 months
c. $437.43 short, 141 months
d. $438.55 short, 180 months
j12 = (.5% * 12)= 6% N = 3 (36 months)
____________________
PV PMT FV
$-350 0 ?
note, i had put PV as 350 not -350 which was incorrect
as the boy is putting the money in the bank (out of pocket) we got that part wrong!
answer=
b. $581.17 short, 210.49 months is the answer
1,000-418.80 = 581.17.
the coolest thing on this one, to find out how long it would take to get to $1,000
all you have to do is, put $1,000 in at FV after the calculation, and then press N and
210.49 months will come up !!!!!!
what does little (i) mean?
means periodic interest rates
id = day iw =week I m = month iq = quarter i sa= semi annual ia= annual (yearly)
turn i sa 3.0% to J2
3.0% X 2 = 6.0%
turn i sa 4.0% to J2
4.0% X 2 = 8.0%
turn i sa 6.5% to J2
6.5% X 2 = 13%
turn i q 3.0% into J4
12%
turn i q 4.0% into J4
16%
turn i q 6.5% into J4
26%
turn i m .2% into J12
2.4%
turn i m .8% into J12
9.6%
turn i m 1.1% into J12
13.2%
turn i d .02 into J365
7.3%
turn i d .02 into J365
10.95%
turn i d .02 into J365
18.25%
turn J2 6.0 into i sa
3.0%
turn J2 6.0 into i sa
4.0%
turn J2 6.0 into i sa
6.5%
what is the difference between J and i?
J = nominal i = periodic
turn J4 = 8.0% into i Q
2.0%
turn J4 = 10.0% into i Q
2.5%
turn J4 16% into i Q
4.0%
turn J 12 6.0% into i m
.5%
turn J 12 8.0% into i m
.66%
turn J 12 13.0% into i m
1.08%
turn J365 8.0 into i d
.219%
turn J365 10.0 into i d
.027%
turn J365 16.0 into i d
.0438
True or False
a monthly periodic rate (i mo) of 3% is equivalent to a nominal rate of j12 = 3% * 12 = 36%?
true
True or False
a daily periodic rate (i d) of .015% is equivalent to a nominal rate of j365 = 0.015 X 365 = 5.475%
true
True or False
a semi annual periodic rate (i sa) is equivalent to a nominal rate of J2 = 1.5* 2 = 3%?
true
true or false
a quarterly periodic rate (i q) of 5.25% is equivalent to a nominal rate of J4 = 5.25 X 4 = 21%
true
i d = 0.02%
PMT = 0 per day
J 365 = ?
saving now $50,000
j365 = 0.02 X 365 = 7.3%
j365 = 7.3% N = 5 years (1825)
________________________
PV PMT FV
$-50,000 $0 ?
FV = $72,023.07
i m = 0.8% PMT = 0 per month J12 = ? saving now $50,000 N = 5 year
j12 = 0.8 X 12 = 9.6%
j12 = 9.6% N = 5 year( 60 month)
_______________________
PV PMT FV
$-50,000 $0 ?
=$80,649.55
i q = 2% PMT = 0 per month J4 = ? saving now $50,000 N=5
4 = 2 X 4 = 8.0%
j4 = 8%
N =5 year (20 years)
_____________________________
PV PMT FV
$-50,000 $0 ?
FV=$74,297.37
i sa = 4% PMT = 0 semi a dual J2 = ? n=5 saving now $50,000
j4 = 2 X 4 = 8.0%
j2 = 8%
N =5 year (10 semi annual)
______________________
PV PMT FV
$-50,000 $0 ?
FV=$74,012.21
iq = 2% PMT = 0 per quarter j4 = ? savings now $50,000 N=5
j4 = 2 X 4 = 8.0%
j4 = 8% N = 5 years (20 quarters)
_______________________________
PV PMT FV
$-50,000 $0 ?
FV = $74,297.37
i sa = 4%
PMT = 0 per semi annual
j2 = ?
n=10
Saving now $50,000
J2 = 4 X 2 = 8%
j2 = 8% N = 5 years (10 semi- annual )
________________________
PV PMT FV
$-50,000 $0 ?
FV = $74,012.21
john bought a townhouse and sold it at the end of the 10th year for $400,000. he earned a return of 6% per annum, compounded annually. what did john buy the home for?
a. $212,250.85
b. $204,750.85
c. $223,357.91
d. $231,120.85
j1 = 6% N= 10
______________________
pv pmt FV
? $0 $400,000
c. $223,357.91 is the correct answer
john gets 20 cents for each candy box that he sells and sells an average of 350 boxes per week. the rate of saving account is J52 = 5%. how much money will john have at the end of 2 years?
a. $ 7,652.58
b. $ 3, 398.31
c. $ 4, 398.31
d. $ 5, 398.31
52 = 5% N = 2 (2 X 52 = 104 weeks)
pv pmt fv
70
answer = $7,652.52
i got this one wrong because for N i put 2 (forgot to do 2 X 52 = 104) NEED TO REMEMBER THIS!!!!
what is one thing you should NOT do when taking your exam?
do not go over your questions twice- do the question and move on, if you second guess yourself it is going to backfire on you.
joe wants to buy an investment home and wants to hold it for 5 years. he wants to earn 5% per annum, compounded
annually at the end of 5 years. what is the maximum price he should pay for the home if it will sell
for $2,500,000?
a. $1,958,815
b. $513,913.25
c. $413,913.25
d. $313,913.25
j1 = 5% N = 5
____________________
pv — pmt — fv
? — 0 —-2,500,000
correct answer is…
$-1,958,815.42
Joe got an interest only loan in the amount of $925,000. The interest rate charged on the loan is 7.5% per annum
compounded semi annually with semi annual payments. if the term of the loan is 2 years, what amount will be due
every 6 months and the last payment after 2 years?
a. $34,687.50, $959,687.50
b. $20,000.33 , $202,000.50
c. $25,000, $201,000.52
d. $23,000.12, $200,000.25
j2 = 7.5% N = 4 (2 X 2= 4)
________________________
PV pmt FV
$925,000 ? -925,000
correct answer is..
a. $34,687.50, $959,687.50
my initial answer was-
= payments -34,648.50
pay on final date -959,687.50?
ok, we were close, but did it again and came up with
-34,687.50 (must have been calculator error)
an interest accruing loan of $150,000 was started with a term of 10 years and an interest rate of 4.5% per annum
comounded monthly. calculate the amount that accumulated at the end of 10 years.
a. $235,048.92
b. $335,048.92
c. $435,048.92
d. $535,048.92
J12 = 4.5% N = (120) 10 years X 12 months
____________________
PV PMT FV
150,000 0 ?
correct answer is
a. $235,048.92
my answer was….. -235,048.92
woooo hooo got it right!!
an interest accruing loan of $150,000 was started with a term of 15 years and an interest rate of 4.5 % per annum, compounded monthly. Calculate the amount that accumulated at the end of 15 years?
a. $294,233.25
b. $335,048.92
c. $435,048.92
d. $535,048.92
J12 = 4.5 N = 15 years X 12 months = 180
______________________
PV PMT FV
$150,000 0 ?
correct answer
a. $294,233.25
my answer = -294,233.25 wooo hooo got it right!!
true of false
a monthly periodic rate (i mo) of 2% is equivalent to a nominal rate of j12 = 2 x 12 = 24% ?
true
true or false
a daily periodic rate (i d) of 0.025% is equivalent to a nominal rate of j365 = 0.025 X 365 = 9.125%?
true
true or false
a semi annual period rate (i sa) of 2.5% is equivalent to a nominal rate of j2 = 2.5 X 2 = 5%?
true
true or false
A quarterly periodic rate (i q) of 3.25% is equivalent to a nominal rate of j4 = 3.25 * 4 = 13%
true
john earns 10 cents for each candy box sells and sells 500 boxes per week. The saving rate is J52 = 5%. how much money will john have at the end of 1 year?
a. $2,664.78
b. $3,398.31
c. $4,398.31
d. $5,398.31
j52 = 5% N = 1 X 52 = 52
___________________
PV PMT FV
0 -50.00 ?
a. $2,664.78 is the correct answer!!
my guess = 2,664.78 wooo hoo we got it right!! except, for the payment we did not put in -50 we put in 50, have to remember that we are MAKING payments (money out of pocket) so it should be a negative
john will save $25 at the end of every week. how much money will have accumulated by the end of the 7th year if interest earned is J52 = 6%.
a. $11,301.18
b. $23,472.25
c. $23,464.25
d. $24,623.25
j52= 6% N = 7 X 52 = 364
____________________
PV PMT FV
0 $-25 ?
a. $11,301.18 is the correct answer !! wooodiee woooo
my guess = 11,301.18 (again we forgot to put in -25 for the payment!! need to clean that up
john received $250 as a gift and will deposit it in the bank account, he will also save $25 at then end of every week. how
much money will have accumulated by the end of the 7th year if interest earned is j52 = 6%
a. $11,681.58
b. $23,472.25
c. $23,640.25
d. $24, 230.25
j52 = 6% n = 7 X 52 = 364
________________
PV PMT FV
-250 -25 ?
a. $11,681.58 is the correct answer
my guess = 10,920.79 got this one wrong!!!!
on this one, i did not put -250, i put 250 for the PV. we have to keep in mind that he PAID 250 to the bank, so that is money out of the pocket!! remember that brother!!
john got $500 from his dad as a gift. he wants to use the money in 2 years to pay 1,000 for a helmet. john has deposited the money in a savings account bearing a periodic interest rate of 0.5 per month, compounded monthly j12 = (0.5 * 12) =6%. will john have enough money to pay for the helmut in 2 years? if he will not have enough money how long will it take
john to have the $1000
a. 435 short/140 months
b. 436.42 short/138 months
c. 437.43 short/141 months
d. 438.55 short/180 months
j12 = 6% n = 2 X 12 = 24
_______________
pv pmt fv
-500 0 ?
b. 436.42 short/138 months is the correct answer
$563.58 is my answer
(1000-563.58 = 436.42)
we got the first part correct, but we didn’t know how to determine the amount of months that would be required (see below)
*****HOW YOU GET THE AMOUNT OF MONTHS IS, YOU NEED TO FIND THE N!!! so we need to remove the N amount and put the $1000 as the FV and from there, we can determine the amount that N would be!!!
what will be the second monthly payment of a $155,000 interest only loan with interest rate of 0.6 % per month
(j12 = 0.6 X 12) and time of the loan is not determined.
a. $930.00
b. $875.00
c. $675.00
d. $775.00
j12 = 0.6 X 12 = 7.2% n = Anytime
_____________________
PV PMT FV
155,000 0 -155,000
correct answer is.. a. $930.00 (all payments will be $930)
so we had no idea how to figure this one out.
1. if the N is not determined, that means you can put anything as N like 1 for example!!!!! this is something we didn’t understand
also, i did not calculate the proper interest amount, i put it as 6% when it needed to be turned into 7.2% (.06 X 12)
an investment that will produce $150,000 in 60 months. what is the investment worth (rounded to the nearest $10 dollars)
if you want to earn 4% per annum, compounded monthly?
a. 122,850
b. 134,780
c. 456,870
d. 121,670
j12 = 4% N = 60
__________________
PV pmt fv
? 0 150,000
a. 122,850 is the correct answer
my guess = -122,850.47 woooo hooooo
what is the value of a $175,000 investment after 36 months (rounded to the nearest dollar) invested at J12 = 3%
a. $161,820
b. $171,460
c. $181,680
d. $191,459
j12 = 3% N = 36
____________________
pv pmt fv
-175,000 0 ?
d. $191,459 is the correct answer, got it right!! wooo wooo
my guess 191,459.00
for an interest only loan, what MUST you remember to write down on your diagram?
pv—-pmt—-fv
50,000–0—(-50,000)
must remember to put (-50,000) because you HAVE to pay the principle back on the last day
