Basis of Calculation for HPA Refund for Borrower-Paid Single-Premium Plans

In the sections below, the following symbols are used:

Symbol Definition
S Starting month of calculation July 2014
Tearn Earning period in months plus 1
n Loan term in months
F Factor for monthly earnings
P Premium amount
p Monthly payment
a Original principal balance
r Annual interest rate / 12
a78 Loan balance at 78% LTV
n78 Number of payments remaining at 78% LTV
M Number of (current) months
EPm Earnings for month

Single Premium Certificates—Borrower Paid

To determine the amount of the refund due for certificates issued on or after July 1, 2014, subtract the earned premium as calculated below from the single premium paid:

Value Calculation
p = a × r × (1+r)n / ((1+r)n-1)
a78 = 78 / 100 × original loan amount / original LTV percentage
n78 = 1n (p / (p - a78 × r)) / 1n (1+r)
F = 1 / (Tearn + 12)

For Earnings for Month (EPm), the calculation rule is as follows:

Monthm Earnings in month m EPm
1 F × P
2 – 12 2 × F × P
13 1.5 × F × P
14 – Tearn F × P
Tearn + 1 p-sum of all previous EPm

For certificates with effective dates prior to July 1, 2014:

The calculation of F (factor for monthly earnings) will depend on s (starting month of calculation) = month in force at July 1, 2014.

Starting month s Factor F
S = 1 (this is listed as a comparison) F = 1 / (Tearn - s + 1 + 12) = 1/( Tearn +12) as described above
S = 2 – 13 F = 1/( Tearn - s + 1 + 12 + 2 - s) = 1 / ( Tearn - 2s +15)
S = 14 – Tearn - 1 F = 1/( Tearn – s + 1 + 0.5) = 1/( Tearn – s + 1.5)
S > = Tearn F = 1

Annual Certificates

Annual premium certificates will be earned over 13 months, with the following distribution, where P is the premium amount paid at the last anniversary:

Month m Earnings Per Month EPm
1 0.5 × P / 12 = P / 24
2 P / 12
3 P / 12
4 P / 12
5 P / 12
6 P / 12
7 P / 12
8 P / 12
9 P / 12
10 P / 12
11 P / 12
12 P / 12
13 0.5 × P / 12 = P / 24

For more information on cancellations and refunds, visit United Guaranty's comprehensive Cancellation Refund page.

For questions about United Guaranty's calculation method, please send an email to UGC:ugcqc or contact your United Guaranty Representative.