Calculation of PMT

CFA Level I Corporate Finance
#1

Hi all,

Suppose a 30-year, $200,000 mortgage loan is taken from bank charging 6% interest, with annual compounding. What are the 30 year-end payments?

I know how to calculate it with the caluclator and the correct answer is $14,529.78.
But how do I do it without the calculator? Is there any formula I missed?

PV = 200,000
i = 0,06 p.a.
n = 30

Isn’t there any solution to get it by pen and paper? :slight_smile:

Cheers
Teemo

#2

Not one that you’re going to want to try to use:

PMT = \frac{iPV\left(i + i\right)^n}{\left(1 + i\right)^n - 1}
1 Like
#3

They LET you bring in a calculator. It will be your only friend during the exam!!! :+1:

#4

All you have to do is set the cash-flow diagram, and it should be pretty straight-forward from there.
Knowing how to set the diagram can be particularly valuable when the cash-flow is significantly more complex (one example being rainbow annuities or something, can’t recall the exact term). Essentially the amount paid changes with time, instead of being fixed.

#5

Thank you so much!
I just want to correct (1+i) in the numerator.

Not to use in the exam just for understanding :slight_smile:
It is not that difficult.

Cheers
Teemo

#6

How? If I don’t know neither the principal nor the overall amount paid at year-end.

#7

The problem assumes you are paying a fixed amount at the end of each year.
Here:

annuity_problem_aug_2_2021
annuity_problem_aug_2_2021652×830 588 KB

1 Like
#8

By the way, I strongly recommend you learn how to set the time diagram. It will prove to be far more useful and versatile than memorizing a shortcut formula, and then forgetting it the day after the exam.
It’s also far more intuitive as well, as you can see from the solution given above.

#9

And don’t forget to set P/Y, C/Y and BEG/END correctly!!! :+1:

1 Like
#10

Thank you for your effort!
So I use the “standard” geometric sum. :ok_hand:

#11

sorry for asking again.
Is there a way to calculate the PMT with payments at the beginning of each year?
How do I adjust the formula?

#12

Divide the RHS by (1+i) in s2000magician’s formula.

On the calculator: 2nd PMT 2nd SET will let you toggle between BEG and END.

ETA: Answer using BEG is 13,707.34

#13

how to do it with calculator?

#14

With the BAII

2nd PMT to make sure you have END
2nd Quit
2nd I/Y
1 P/Y Enter :arrow_down:, 1 C/Y Enter
2nd Quit
2nd FV to clear the TVM registers
30 N 6 I PV 200,000 FV 0 CPT PMT -14,529.7823