Question

How much principal is repaid in the first payment interval on a $100,000 25-year mortgage? The mortgage is amortized over 25 years and the payments are monthly. The interest rate is 6% compounded semi-annually.

Answer 1

EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100

? = ((1+6/(2*100))^2-1)*100

Effective Annual Rate% = 6.09

EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100

6.09 = ((1+Stated rate%/(12*100))^12-1)*100

Stated rate% = 5.9263

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

C = Cash flow per period

i = interest rate

n = number of payments

100000= Cash Flow*((1-(1+ 5.9263/1200)^(-25*12))/(5.9263/1200))

Cash Flow = 639.8

	Monthly rate(M)=	yearly rate/12=	0.49%	Monthly payment=	639.80
Month	Beginning balance (A)	Monthly payment	Interest = M*A	Principal paid	Ending balance
1	100000.00	639.80	493.86	145.95	99854.05

Where

Interest paid = Beginning balance * Monthly interest rate

Principal = Monthly payment – interest paid

Ending balance = beginning balance – principal paid

Beginning balance = previous Month ending balance