P2.T5.108. Mortgage payment factor

[David Harper CFA FRM]

AIMs: Describe the key attributes that define mortgages. Calculate the mortgage payment factor. Understand the allocation of loan principal and interest over time for various loan types. (Fabozzi)

Questions:

108.1. Sally has been approved for a 30-year fixed rate (fully-amortizing) mortgage with an interest rate of 3.48% per annum. However, she can also select a 15-year mortgage with an stunningly low interest rate of 2.52%. If the loan balance has yet to be determined but will be the same with either mortgage, what is the ratio of the monthly payment (principal plus interest) on the 15-year mortgage to the monthly payment on the 30-year mortgage?

a. 72%
b. 149%
c. 225%
d. 278%

108.2. For 2012, the conforming loan balance limit continues to be $417,000 (for the second year in a row). If a 30-year fully-amortizing loan is originated with exactly this balance, and the 30-year fixed mortgage rate is 3.6% per annum, after the first two (2) monthly mortgage payments how much PRINCIPAL will the borrower have cumulatively paid?

a. $652.64
b. $989.17
c. $1,035.23
d. $1,291.68

108.3. A 30-year 5/1 hybrid ARM has an initial loan balance of $110,000 with a fixed rate of 3.00% per annum. After five years, when the balance is reduced to $97,797.00, the rate resets to 4.80%. What is, respectively, the total monthly payment (principal plus interest) during the first sixty months and on the sixty-first (61st) month?

a. $489.25 (1-60th) and $503.29 (61st)
b. $489.25 (1-60th) and $577.13 (61st)
c. $463.76 (1-60th) and $513.11 (61st)
d. $463.76 (1-60th) and $560.37 (61st)

Answers:

• Here in forum

 

[sl]

Hello David,

For Q 108.3,
During the fixed portion of the ARM while we compute the mortgage payment factor shouldn't the value of T=60 months instead of 360 as is mentioned in the PQ?

Thanks
Sundeep

 

[David Harper CFA FRM]

Hi Sundeep,

Good question, it gave me enough pause to refer back to the source. It looks like the Q&A is correct as-is. First, note that if we did use T=60, we'd be as-if fully amortizing the loan in five years and the selling appeal of low initial monthly would be lost [for T=60, I get $1,976.56 per month (versus $463.76)] and at the end of five years, there would be no remaining principal. So, this would be a 5-year fixed loan.

FYI, here is the underlying spreadsheet I used for the question (two tabs): http://db.tt/vQNm6GDw

And the source (emphasis mine):

"For amortizing ARM loans, the initial payment is calculated at the initial note rate for the full 360-month term. At the first reset, and at every subsequent adjustment, the loan is recast, and the monthly payment schedule is recalculated using the new note rate and the remaining term of the loan. For example, payments on a five-year hybrid ARM with a 5.5% note rate would initially be calculated as a 5.5% loan with a 360-month term. If the loan resets to a 6.5% rate after five years (based on both the underlying index and the loan’s margin), the payment is calculated using a 6.5% note rate, the remaining balance in month 60, and a 300-month term. In the following year, the payment would be recalculated again using the remaining balance and prevailing rate (depending on the performance of the index referenced by the loan) and a 288-month term. In this case, the loan’s initial monthly payment would be $568; in month 60, the loan’s payment would change to $624, or the payment at a 6.5% rate for 300 months on a $92,460 remaining balance. The payments on an interest-only hybrid ARM are similar to those of a fixed rate, interest-only loan. Using the rate structure described above, an interest-only 5/1 hybrid ARM would have an initial payment of $458. After the 60-month fixed rate, interest-only period, the monthly payments would reset at $675, an increase of roughly 47%. This increase represents the payment shock discussed previously. Depending on the loan’s margin and the level of the reference index, borrowers seeking to avoid a sharp increase in monthly payments often refinance their loans into cheaper available products. The desire to mitigate payment shock is also largely responsible for the growth in hybrid ARMs with noncontiguous resets. Since these loans essentially separate the rate reset and payment recast, the payment increases are spread over two periods, reducing the impact of a large one-time increase in payment." Fabozzi MBS 2nd Edition, p 15

Hope that helps, thanks!

 

[sl]

It sure did help, thanks!

 

[mosta143]

hi sir i am very thankful to you to give your valuable time for us