2
$\begingroup$

From The problem statment: What is the monthly payment for a $800,000 mortgage for the first 119 payments that is due in 10 years, has a 25 year amortization, at 5% interest? What is the amount of the 120th payment?

PV: 800,000 from loan is due in 10 years,

and 25 amortization at 5% then, from here I have

Monthly interest I/Y:

5/12 = 0.42

Amount of payments N:

25*12= 300 payments

Then I have:

N      I/Y        PV        PMT     FV     
300     0.42      800K       ?       0

PMT= -4,699.09

Now at payment 119 I paid : -559,192.19 each payment of -4,699.09

and at 120 I will paid: -563,891 and left a balloon payment of 236,108.71 = 800k-563,891

Question: Is it my work correct or I'm missing something? Thanks

$\endgroup$
0
1
$\begingroup$

The monthly interest is not 1/12 of the annual interest but 1 less than the 12-th root of 1 more, i.e.,

$$(1+0.05)^{1/12}-1=0.004074...$$

or slightly less than 0.41 percent.

$\endgroup$
3
  • $\begingroup$ If I change, and use 0.4074. My procedure was correct? $\endgroup$
    – Electro82
    Dec 10 '15 at 22:44
  • $\begingroup$ Why is it 1 less than the 12th root of one more? Why does the -1 come into play? $\endgroup$
    – K. Gibson
    Mar 20 '16 at 17:29
  • $\begingroup$ In compound interest, it is the total (principal, represented as 1 or 100 percent, plus interest) that is raised to the power of the number of periods (in this case 12). The 1 between the brackets represents adding the principal to the interest. The minus 1 outside the brackets is the inverse operation because I was trying to obtain the effective interest. $\endgroup$ Mar 21 '16 at 9:45

Not the answer you're looking for? Browse other questions tagged or ask your own question.