Calculating the Size of Payments on a Fixed- Rate Mortgage

CFA Level I Quant
#1

You are planning to purchase a $120,000 house by making a down payment of $20,000 and borrowing the remainder with a 30- year fixed- rate mortgage with monthly payments. The first payment is due at t = 1. Current mortgage interest rates are quoted at 8 percent with monthly compounding. What will your monthly mortgage payments be?

All right explain to me why my logic is not right:

Im paying $20000 today so this should be PV, The total payment in the future is $120000, as the rate is month would be 0,08/12 = 0,006667 and t=30*12=360

When I put this in my HP12c:

PV = 20.000 CHS

FV = 120.000

I = 8 ENTER 12 /

N = 12 ENTER 30 X

PMT = 66,235

but the answer is the book is $733,76 how is my logic not right?

#2

You need 120,000 TODAY to buy the house, but you only have 20,000. The other 100,000 is what you are borrowing TODAY which you will repay with monthly instalments.

PV =100,000 FV=0 I= 8 ENTER 12/ N=12 ENTER 30 X (Remember, I am a BAII man, so I’m guessing on the HP inputs)

#3

The question is about the loan, not about the purchase of the house.

You can look at this from the lender’s (bank’s) point of view or from the borrower’s (home buyer’s) point of view. The value of the loan today is $100,000 and in 30 years $0. The down payment doesn’t come into the calculation. (Well, it does, sort of: $100,000 = $120,000 − $20,000.)

From the lender’s point of view:

PV = −100,000

FV = 0

n = 30 × 12 = 360

i = 8% ÷ 12 = 0.6667%

Solve for PMT = 733.76

From the borrower’s point of view:

PV = 100,000

FV = 0

n = 30 × 12 = 360

i = 8% ÷ 12 = 0.6667%

Solve for PMT = −733.76

2 Likes
#4

Thank you, that helped a lot!

#5

Thank you so much you have been helping me a lot!

#6

I’m on this right now and I can’t even understand the formula in curriculum as they are using pv = a(1-(1+r)n/r) which is obvious but they continue with present value annuity factor = 1 - 1/1+(rs/m)mN/rs/m - where is formula come from? there are no mention about this formula in curriculum? What I’ve missed?

thank you beforehand

#7

The formulas are the same

rs/m = 0,08/12 and mn = 12*30

You need to do that because It compounds monthly instead of annually.

Althorugh I recommend you use a financial calculator as it is far more intuitive (It`s impossible to remember all this TVM formulas), the only one you really need to know is the value of a perpetuity.

#8

It comes from arithmetic principles.

That is the PVIFA component in this equation:

LA = PMT * PVIFA LA = Loaned ammount
PMT = Payment

So, if you take your loaned amount divided by the PVIFA you’ll get your monthly mortgage payment (or your otherwise specified periodical equivolent payment).

#9

thank you but if I understand right, calculator won’t help if I cant remember the proper formula or not?

#10

thank you I was thinking the same way but I couldn’t find the exact formula so I thought I’ve missed something.

#11

Financial calculators have built-in functions for computing present value, future value, and periodic payment. You don’t need to know the formulae to be able to do these calculations.

#12

I have nothing against the CFA curriculum including these formulas though so a candidate can at least understand how to do it without a financial calculator.

At least that’s what we had to do when I was a freshman in college. Our teacher didn’t let us use anything other than simple maths.

#13

Thank you very much, that’s very great news! :sunglasses:

#14

Is this information still relevant?

#15

Payments should be secure and encrypted. When you add a card to your online payment account, there should be no way for someone to access your money without your knowledge.

#16

FWIW, as it should, Excel produces the same answer: =PMT(0.08/12, 360, -100000).