Actuarial problem. Amortization Problem in a 25 year period at 5%

Question

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

Answer 1

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.