(a) Introduction. Creditors are required to disclose a series of
total-annual-loan-cost rates for each reverse mortgage transaction.
This appendix contains the equations creditors must use in computing
the total-annual-loan-cost rate for various transactions, as well
as instructions, explanations, and examples for various transactions.
This appendix is modeled after Appendix J of this part (Annual Percentage
Rates Computations for Closed-End Credit Transactions); creditors
should consult Appendix J of this part for additional guidance in
using the formulas for reverse mortgages.
(b) Instructions and equations for the total-annual-loan-cost
rate.
(1) General rule. The total-annual-loan-cost
rate shall be the nominal total-annual-loan-cost rate determined by
multiplying the unit-period rate by the number of unit periods in
a year.
(2) Term of the transaction. For purposes of
total-annual-loan-cost disclosures, the term of a reverse mortgage
transaction is assumed to begin on the first of the month in which
consummation is expected to occur. If a loan cost or any portion of
a loan cost is initially incurred beginning on a date later than consummation,
the term of the transaction is assumed to begin on the first of the
month in which that loan cost is incurred. For purposes of total-annual-loan-cost
disclosures, the term ends on each of the assumed loan periods specified
in section 1026.33(c)(6).
(3) Definitions of time intervals.
(i) A period is the interval
of time between advances.
(ii) A common period is any period
that occurs more than once in a transaction.
(iii) A standard interval of time is a day, week, semimonth, month, or a multiple of a week or a month
up to, but not exceeding, one year.
(iv) All months shall be considered
to have an equal number of days.
(4) Unit period.
(i) In all transactions other than single-advance,
single-payment transactions, the unit period shall be that common
period, not to exceed one year, that occurs most frequently in the
transaction, except that:
(A) If two or more common periods occur with
equal frequency, the smaller of such common periods shall be the unit
period; or
(B) If there
is no common period in the transaction, the unit period shall be that
period which is the average of all periods rounded to the nearest
whole standard interval of time. If the average is equally near two
standard intervals of time, the lower shall be the unit period.
(ii)
In a single-advance, single-payment transaction, the unit period shall
be the term of the transaction, but shall not exceed one year.
(5) Number of unit periods between two given dates.
(i) The number of days between two dates
shall be the number of 24-hour intervals between any point in time
on the first date to the same point in time on the second date.
(ii) If the unit period
is a month, the number of full unit periods between two dates shall
be the number of months. If the unit period is a month, the number
of unit periods per year shall be 12.
(iii) If the unit period is a semimonth
or a multiple of a month not exceeding 11 months, the number of days
between two dates shall be 30 times the number of full months. The
number of full unit periods shall be determined by dividing the number
of days by 15 in the case of a semimonthly unit period or by the appropriate
multiple of 30 in the case of a multimonthly unit period. If the unit
period is a semimonth, the number of unit periods per year shall be
24. If the number of unit periods is a multiple of a month, the number
of unit periods per year shall be 12 divided by the number of months
per unit period.
(iv) If the unit period is a day, a week, or a multiple of a week,
the number of full unit periods shall be determined by dividing the
number of days between the two given dates by the number of days per
unit period. If the unit period is a day, the number of unit periods
per year shall be 365. If the unit period is a week or a multiple
of a week, the number of unit periods per year shall be 52 divided
by the number of weeks per unit period.
(v) If the unit period is a year, the
number of full unit periods between two dates shall be the number
of full years (each equal to 12 months).
(6)
Symbols. The symbols used to express the terms of a transaction in the equation
set forth in paragraph
(b)(8) of this appendix are defined as follows:
Symbols
| Aj |
= |
The amount of each periodic or lump-sum
advance to the consumer under the reverse-mortgage transaction. |
| i |
= |
Percentage rate of the total annual loan
cost per unit period, expressed as a decimal equivalent. |
| j |
= |
The number of unit periods until the jth
advance. |
| n |
= |
The number of unit periods between consummation
and repayment of the debt. |
| Pn |
= |
Min (Baln, Valn).
This is the maximum amount that the creditor can be repaid at the
specified loan term. |
| Baln |
= |
Loan balance at time of repayment, including
all costs and fees incurred by the consumer (including any shared
appreciation or shared equity amount) compounded to time n at the
creditor’s contract rate of interest. |
| Valn |
= |
Val0 (1 + Σ)y, where
Val0 is the property value at consummation, Σ is the assumed
annual rate of appreciation for the dwelling, and y is the number
of years in the assumed term. Valn must be reduced by the
amount of any equity reserved for the consumer by agreement between
the parties, or by 7 percent (or the amount or percentage specified
in the credit agreement), if the amount required to be repaid is limited
to the net proceeds of sale. |
| Σ |
= |
The summation operator. |
Symbols used
in the examples shown in this appendix are defined as follows:
Symbols used
in the examples shown in this appendix are defined as follows
| $$
\require{enclose}
\mathrm{FV_{\enclose{actuarial}{x}}\text{}i}
$$
FVx i
|
= |
The future value of 1 per unit period for
x unit periods, first advance due immediately (at time = 0, which
is consummation). |
| |
= |
$$
\mathrm{\displaystyle\sum_{j=0}^{x-1} (1+i)^{x-j}}
$$
x−1
Σ (1 + i)x−j
j=0
|
| |
= |
$$
\begin{align*}
&\mathrm{(1 + i)^x + (1 + i)^{x-1}}\\
&+ \mathrm{(1 + i)^1}
\end{align*}
$$
(1 + i)x + (1 + i)x −1
+ (1 + i)1
|
| or |
|
|
| |
= |
$$
\mathrm{\frac{(1+ i)^n - 1}{i} \times (1 + i)}
$$
(1 + i)n − 1 × (1 + i)
i
|
| w |
= |
The number of unit periods per year. |
| I |
= |
wi × 100 = the nominal total-annual-loan-cost
rate. |
(7)
General equation. The total-annual-loan-cost
rate for a reverse-mortgage transaction must be determined by first
solving the following formula, which sets forth the relationship between
the advances to the consumer and the amount owed to the creditor under
the terms of the reverse-mortgage agreement for the loan-cost rate
per unit period (the loan-cost rate per unit period is then multiplied
by the number of unit periods per year to obtain the total-annual-loan-cost
rate I; that is, I = wi):
General equation
| |
$$
\mathrm{\displaystyle\sum_{j=0}^{n-1} A_j (1 + i)^{n-j} = P_n}
$$
n−1
Σ Aj (1 + i)− = Pn
j=0
|
(8) Solution of general equation by iteration process.
(i) The general equation in paragraph
(b)(7) of this appendix, when applied to a simple transaction for
a reverse-mortgage loan of equal monthly advances of $350 each, and
with a total amount owed of $14,313.08 at an assumed repayment period
of two years, takes the special form:
General equation
$$
\require{enclose}
\mathrm{P_n = 350\text{ }FV_{\enclose{actuarial}{24}}\text{}i}
$$
Pn = 350 FV24 i
|
| or |
$$
\mathrm{P_n = 350 \times \Bigg[ \frac{(1+i)^n -1}{i} \times (1+i) \Bigg]}
$$
Pn = 350 × [(1 + i)n − 1 × (1 + i)]
i
|
Using the iteration procedures found in steps 1 through
4 of (b)(9)(i) of appendix J of this part, the total-annual-loan-cost
rate, correct to two decimals, is 48.53 percent.
(ii) In using these iteration procedures,
it is expected that calculators or computers will be programmed to
carry all available decimals throughout the calculation and that enough
iterations will be performed to make virtually certain that the total-annual-loan-cost
rate obtained, when rounded to two decimals, is correct. Total-annual-loan-cost
rates in the examples below were obtained by using a 10-digit programmable
calculator and the iteration procedure described in appendix J of
this part.
(9) Assumption for discretionary cash advances. If the consumer controls the timing of advances made after consummation
(such as in a credit-line arrangement), the creditor must use the
general formula in paragraph (b)(7) of this appendix. The total-annual-loan-cost
rate shall be based on the assumption that 50 percent of the principal
loan amount is advanced at closing, or in the case of an open-end
transaction, at the time the consumer becomes obligated under the
plan. Creditors shall assume the advances are made at the interest
rate then in effect and that no further advances are made to, or
repayments made by, the consumer during the term of the transaction
or plan.
(10) Assumption for variable-rate reverse-mortgage
transactions. If the interest rate for a reverse-mortgage transaction
may increase during the loan term and the amount or timing is not
known at consummation, creditors shall base the disclosures on the
initial interest rate in effect at the time the disclosures are provided.
(11) Assumption for closing costs. In calculating
the total-annual-loan-cost rate, creditors shall assume all closing
and other consumer costs are financed by the creditor.
6-6022
(c) Examples of total-annual-loan-cost
rate computations.
(1) Lump-sum
advance at consummation.
Lump-sum advance to consumer at consummation:
$30,000
Total of consumer’s loan costs financed
at consummation: $4,500
Contract interest rate: 11.60%
Estimated time of repayment (based on life
expectancy of a consumer at age 78): 10 years
Appraised value of dwelling at consummation:
$100,000
Assumed annual dwelling appreciation rate:
4%
Equation
| P10 = Min (103,385.84, 137,662.72) |
$$
\begin{align*}
30,000(1+\mathrm{i})^{10-0} & + \mathrm{\sum_{j=0}^{9} 0 (1+i)^{10-j}} \\
&= 103,385.84
\end{align*}
$$
9
30,000(1 + i)10 −0 + Σ 0(1 + i)10−j
j = 0
= 103,385.84
|
| i = .1317069438 |
| Total-annual-loan-cost
rate (100(.1317069438 × 1)) = 13.17% |
(2) Monthly advance beginning at consummation.
Monthly advance to consumer, beginning at
consummation: $492.51
Total of consumer’s loan costs financed
at consummation: $4,500
Contract interest rate: 9.00%
Estimated time of repayment (based on life
expectancy of a consumer at age 78): 10 years
Appraised value of dwelling at consummation:
$100,000
Assumed annual dwelling appreciation rate:
8%
Equation
| P120 = Min (107,053.63, 200,780.02) |
| $$
\begin{align*}
492.51 \times & \Bigg[ \frac{(1+\mathrm{i})^{120} -1 }{\mathrm{i}} \times (1+\mathrm{i}) \Bigg] \\
& = 107,053.63
\end{align*}
$$
492.51 × [(1 + i)120 − 1 × (1 + i)]
i
= 107,053.63
|
| i = .009061140 |
| Total-annual-loan-cost
rate (100(.009061140 × 12)) = 10.87% |
(3) Lump-sum advance at consummation and monthly
advances thereafter.
Lump-sum advance to consumer at consummation:
$10,000
Monthly advance to consumer, beginning at
consummation: $725
Total of consumer’s loan costs financed
at consummation: $4,500
Contract rate of interest: 8.5%
Estimated time of repayment (based on life
expectancy of a consumer at age 75): 12 years.
Appraised value of dwelling at consummation:
$100,000
Assumed annual dwelling appreciation rate:8%
Equation
$$
\begin{align*}
\mathrm{P_{144}} & = \mathrm{Min} \text{ } (221,818.30, 234,189.30) \\
& 10,000(1+ \mathrm{i})^{140-0} \\
& + \mathrm{\sum_{j=0}^{143}} \quad 725(1+\mathrm{i})^{144-\mathrm{j}} = 221,818.30
\end{align*}
$$
P144 = Min (221,818.30, 234,189.82)
10,000(1 + i)140−0
143
+ Σ 725(1 + i)144 −j = 221,818.30
j = 0
|
| i = .007708844 |
| |
| Total-annual-loan-cost
rate (100(.007708844 × 12)) = 9.25% |
6-6023
(d) Reverse-mortgage
model form and sample form.
(1) Model form.
TOTAL-ANNUAL-LOAN-COST
RATE
TOTAL-ANNUAL-LOAN-COST
RATE
| Loan Terms |
Monthly Loan Charges |
| Age of youngest
borrower: |
Servicing fee: |
| Appraised
property value: |
|
| Interest rate: |
Other Charges |
| Monthly advance: |
Mortgage insurance: |
| Initial draw: |
Shared appreciation: |
| Line of credit: |
|
| |
Repayment Limits |
| Initial Loan Charges |
| Closing costs: |
|
| Mortgage insurance premium: |
|
| Annuity cost: |
|
Total-Annual-Loan-Cost
Rate
| |
Total-Annual-Loan-Cost Rate |
| Assumed
Annual Appreciation |
2-year loan term |
[[ ]-year loan term] |
[ ]-year loan term |
[ ]-year loan term |
| 0% |
|
[ ] |
|
|
| 4% |
|
[ ] |
|
|
| 8% |
|
[ ] |
|
|
The cost of any reverse-mortgage loan depends on how long
you keep the loan and how much your house appreciates in value. Generally,
the longer you keep a reverse mortgage, the lower the total-annual-loan-cost
rate will be.
This table shows the estimated cost of your reverse-mortgage
loan, expressed as an annual rate. It illustrates the cost for three
[four] loan terms: 2 years, [half of life expectancy for someone your
age,] that life expectancy, and 1.4 times that life expectancy. The
table also shows the cost of the loan, assuming the value of your
home appreciates at three different rates: 0%, 4%, and 8%.
The total-annual-loan-cost rates
in this table are based on the total charges associated with this
loan. These charges typically include principal, interest, closing
costs, mortgage insurance premiums, annuity costs, and servicing costs
(but not costs when you sell the home).
The rates in this table are estimates. Your actual cost
may differ if, for example, the amount of your loan advances varies
or the interest rate on your mortgage changes.
SIGNING AN APPLICATION OR RECEIVING THESE DISCLOSURES
DOES NOT REQUIRE YOU TO COMPLETE THIS LOAN
(2) Sample Form.
TOTAL-ANNUAL-LOAN-COST
RATE
TOTAL-ANNUAL-LOAN-COST
RATE
| Loan Terms |
|
Monthly Loan Charges |
| Age of youngest
borrower: |
75 |
Servicing fee: None |
| Appraised
property value: |
$100,000 |
|
| Interest rate: |
9% |
Other Charges |
| Monthly advance: |
$301.80 |
Mortgage insurance:
None |
| Initial draw: |
$1,000 |
Shared appreciation:
None |
| Line of credit: |
$4,000 |
|
| Initial Loan Charges |
|
Repayment Limits |
| Closing costs: |
$5,000 |
Net proceeds estimated
at |
| Mortgage insurance premium: |
None |
93% of projected home
sale |
| Annuity cost: |
None |
|
TOTAL-ANNUAL-LOAN-COST
RATE
| |
Total-Annual-Loan-Cost Rate |
| Assumed Annual Appreciation |
2-year loan term |
[6-year loan term] |
12-year loan term |
17-year loan term |
| 0% |
39.00% |
[14.94%] |
9.86% |
3.87% |
| 4% |
39.00% |
[14.94%] |
11.03% |
10.14% |
| 8% |
39.00% |
[14.94%] |
11.03% |
10.20% |
The cost of any reverse-mortgage loan depends on how long
you keep the loan and how much your house appreciates in value. Generally,
the longer you keep a reverse mortgage, the lower the total-annual-loan-cost
rate will be.
This table shows the estimated cost of your reverse-mortgage
loan, expressed as an annual rate. It illustrates the cost for three
[four] loan terms: 2 years, [half of life expectancy for someone your
age,] that life expectancy, and 1.4 times that life expectancy. The
table also shows the cost of the loan, assuming the value of your
home appreciates at three different rates: 0%, 4%, and 8%.
The total-annual-loan-cost rates
in this table are based on the total charges associated with this
loan. These charges typically include principal, interest, closing
costs, mortgage insurance premiums, annuity costs, and servicing costs
(but not disposition costs—costs when you sell the home).
The rates in this table are
estimates. Your actual cost may differ if, for example, the amount
of your loan advances varies or the interest rate on your mortgage
changes.
SIGNING AN APPLICATION OR RECEIVING THESE DISCLOSURES
DOES NOT REQUIRE YOU TO COMPLETE THIS LOAN
