Question

(4 points) Consider a 2-year mortgage loan that is paid back semi-annually. The semi-annually compounded mortgage rate is 5%. The principal is $1000. a) (1 point) Calculate the semi-annual coupon. b) (3 points) How much of the coupon is interest payment and how much is principal repayment in 0.5 year, in 1 year, in 1.5 years, and in 2 years? Also calculate the (post- coupon) notional value of the outstanding principle for these four dates.

Answer 1

a

PVordinary Annuity

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

1000= Cash Flow*((1-(1+ 5/200)^(-2*2))/(5/200))

Cash Flow = 265.82 = semi-annual coupon

b

	Semi Annual rate(M)=	yearly rate/2=	2.50%	Semi Annual payment=	265.82
Half year	Beginning balance (A)	Semi Annual payment	Interest = M*A	Principal paid	Post coupon notional value
1	1000.00	265.82	25.00	240.82	759.18
2	759.18	265.82	18.98	246.84	512.34
3	512.34	265.82	12.81	253.01	259.33
4	259.33	265.82	6.48	259.33	0.00

Where

Interest paid = Beginning balance * Semi Annual interest rate

Principal = Semi Annual payment – interest paid

Ending balance = beginning balance – principal paid

Beginning balance = previous Half year post coupon notional value