Question

I was looking at the solution to the following question on this site. I could not understand why use 12 when working out the NPER. Since the monthly payments start 1 month after should you not use 11?

Question 3. (a) A family member is thinking about funding his granddaughter’s university education in 8 years when she is expected to enrol at UWI, St. Augustine. He opens a special savings account, where he can receive a lump sum in 8 years. If he is desirous of receiving $60,000 in 8 years when his granddaughter is matriculating, how much would you advise him to deposit in the savings account monthly if annual interest rate is 6%? Show all working.

(b) As a prospective home-owner, you have researched the housing market and you are attracted by two offers. Two $380,000 real estate properties with two different Mortgage (amortization) schedules.

Schedule A requires a down payment of 10% while Schedule B requires a down payment of 12%. If the mortgage is over a period of 20 years at an annual mortgage rate of 7%, what would be the monthly repayment amount for both schedules? Assume that the monthly repayment starts 1 month after the mortgage contract is signed and the down payment made. Show all calculations.

assumption monthly deposits are end of the month |

total payments period n = 8*12 n or NPER = 96 |

Rate given as 6% or 0.06 hence monthly rate is 6%/12 = 0.005 |

Future value / Goal is 60000 |

Find Monthly payments/ annuity (PMT) |

Future value of Ordinary Annuity formula |

annuities* (((1+i)^n)-1) / i |

Substituting values we can find annuity / montthly payments |

OR |

Method 2 |

You can use the PMT function in excel |

PMT (Rate, NPER, PV, FV, Type) |

PMT(6%/12,8*12,,60000) |

488.49 is the monthly depsoit to achiev the goal of 60000 in 8yrs |

b |

Schedule A |

total payments period n = 20*12 n or NPER = 240 |

Rate given as 6% or 0.06 hence monthly rate is 7%/12 = 0.005833333 |

Present value is Loan = purchase cost - down payment = 342000 |

Find Monthly payments/ annuity (PMT) |

PMT = Present Value / [ 1- ( 1+r)^-n]/ r |

Substituting values we can find annuity / montthly payments |

OR |

Method 2 |

You can use the PMT function in excel |

PMT (Rate, NPER, PV, FV, Type) |

PV is entered as a negative figure |

PMT(7%/12,12*20,-342000) |

2651.52 is the monthly repayment |

The only change in
Schedule B is the present value of loan |

Present value is Loan = purchase cost - down payment = 334400 |

PMT(7%/12,12*20,-334400) |

2592.60 is the monthly repayment |

Answer #1

assume a more easy case, let's say instead of monthly payments there were semi-annual payments starting at the end of 6 months from now and the period for semi-annual payments was 2 years

NPER would be calculated = 2*2 = 4

for period of 2 years:

at the end of 0.5 years : payment 1

at the end of 1 year : payment 2

at the end of 1.5 year : payment 3

at the end of 2 years : payment 4

so we can see that altogether there are 4 payments within these 2 years which is the same as calculated through NPER

the same case applies to the above questions

No. of payments would be = NPER = no. of years*12 ( in case of monthly payments)

Please use Excel
to answer the following TVM questions. You can use this spreadsheet
to set up your calculations if you so desire. Unless indicated
otherwise, assume that all of the problems are ordinary annuities
(payment made at the end of the
period).
Part 3
I am going to
buy a car. I will finance the whole purchase (no down payment) with
a new car loan that has a 6-year term. My monthly payments will be
$392/mth and the annual...

Please create a Variable Interest Rate Loan Amortization
schedule with the columns: Year, Amount owed on the principal at
the beginning of the year, Annuity payment, Interest portion of the
annuity, Repayment of the principal portion of the annuity,
outstanding loan balance at year end
For the following:
You obtain a $6,000 loan from a furniture dealer at a variable
interest rate. The loan payments is adjusted every year based on
the annuity amount implied by interest rate of year...

Question 3. (a) A family member is thinking about
funding his granddaughter’s university education in 8 years when
she is expected to enrol at UWI, St. Augustine. He opens a special
savings account, where he can receive a lump sum in 8 years. If he
is desirous of receiving $60,000 in 8 years when his granddaughter
is matriculating, how much would you advise him to deposit in the
savings account monthly if annual interest rate is 6%? Show all
working....

1. Find the present value of the annuity given the following. a)
36 monthly payments of $250 in an account where the interest rate
is 3.5% compounded monthly.
PMT = 250, i = 0.035/12= 0.002916, n = 36 X 12 = 36
?? = ( 250[1-(1+0.002916)-342])/0.002916
PV = ( 24.879080)/0.002916
PV = 8531.920438 = $8,531.90
b) 60 weekly payments of $125 in an account where the interest
rate is 5% compounded weekly.
PMT = 125, i = 0.05/52= 0.000961, n...

Nalu and Kamaile take-out a mortgage in the amount of $260000 to
purchase an apartment as their principal place of residence. They
are able to obtain a 15-year mortgage at a fixed rate of 6%. Below,
you will be asked for the amount of their monthly payment and for a
aggregated amount of interest that they paid.
Clearly, this is a TVM (time value of money) problem, so get
started by completing the table of "TVM Basic Data"
c
n...

As per The Economist (June 24, 2017), the Argentinian
government issued its first 100‐year bond, with cash flows
denominated in dollars. The bond thus now matures in,
for simplification purposes, 97 years. The current bond has a
$1,000 face value and the following monthly, end‐ofmonth
coupon payments: $10/ month for 47 years, $30/month for 20 years,
and then $50/month for 30 years. As
Argentina has defaulted on its bonds six times in the past 100
years, you decide that a...

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BGN or END MODE ( choose one ) P/Y =
N= ?
I/Y=
PV=
PMT=
FV=
CPT , N =
Can you explain how you computed it for compunded monthly.
2. How many years does it take for $1,000 to grow to be
$1,500, if interest rate is 12%?
BGN or END MODE ( choose one ) P/Y =
N= ?...

I am having some trouble visualizing this present value question
and have already put it on a timeline, but it's still not clear. I
think I may be making it more complex than it really is, but here
is the question and then I will explain why I am having
problems.
At an annual interest rate of 6%, which would you prefer - three
annual year-end cash flows of $250 each with the first cash flow
one year from today...

You bought a house for 150,000. The bank required a
20% down payment and gave you a 30-year mortgage loan for the
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monthly repayment schedule. What is your monthly
payment? After 18 years of payments, how much do you
still owe?

Question 2
2a) Suppose a risk-free bond promises
to pay $2,249.73 in 4 years. If the going risk-free
interest rate is 3.5%, how much is the bond worth
today?
Nper
Rate
PMT
FV
PV
2b) Suppose you can buy a U.S. Treasury
bond which makes no payments until the bond matures 10 years from
now, at which time it will pay you $1,000. What interest rate would
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Nper
PMT
PV
FV
Rate...

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