Question

Consider a ARM that will adjust annually, based on the one-year constant maturity U. S. Treasury Bill rate. Further, assume that this mortgage has a starting interest rate of two percent (2%) for the first year. Additionally, the margin on this mortgage is 250 basis points. Finally, this loan has a 1.50% annual interest rate cap, and a 5.00% lifetime interest cap. At the time that the mortgage is offered, the one-year constant maturity T-Bill rate is 1.50%. If the T-Bill rate falls to 1.25% at the first change/reset date, what is the interest rate on this ARM for the second year? Show your work and give a brief explanation regarding your answer. If the T-Bill rate remains constant at 1.25% at the second change/reset date, what is the interest rate on the ARM for the third year? Show your work and give a brief explanation regarding your answer. If the T-Bill rate increases to 4.00% at the third reset date, what is the interest rate on the ARM for the fourth year? Show your work and give a brief explanation regarding your answer.

Answer 1

Interest Rate in year 1	2%
Annual interest rate cap	1.5%
Maximum Rate allowed in year 2=2+1.5=	3.50%
Margin on the mortgage=250 basis point	2.5%
T-bill Rate at the time of first adjustment	1.25%
Interest rate can be charged in year2 based on T-bill rate	3.75%	(1.25+2.5)
Maximum allowed in year 2 based on annual Cap=2+1.5	3.50%
Interest rate to be charged in Year 2	3.50%
Interest Rate
Interest rate can be charged in year3 based on T-bill rate	3.75%	(1.25+2.5)
Maximum allowed in year 3 based on annual Cap	5%	(3.5+1.5)
Interest rate to be charged in Year 3	3.75%
T-bill Rate at the time of third reset	4%
Interest rate in year 4 as per margin=4+2.5	6.50%
Interest rate in year 4 as per annual cap=3.75+1.5	5.25%
Lifetime Cap on interest rate	5%
Interest Rate to be charged in year 4	5%
Interest rate to be charged in Year 2	3.50%
Interest rate to be charged in Year 3	3.75%
Interest Rate to be charged in year 4	5%