Question

Consider a 30 years，$115,000 fixed-rate mortgage with a nominal annnal rate of 4.35 percent. All payments are made at the end of each month. What is the remaining balance on the mortagage after 5 years ?

Answer 1

PV of annuity for making pthly payment
P = PMT x (((1-(1 + r) ^- n)) / i)
Where:
P = the present value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the effective interest rate (also known as the discount rate)
i=nominal Interest rate
n = the number of periods in which payments will be made
Nominal Rate	4.35%
Compounding	Monthly
Effective rate=	((1+4.35%/12)^12)-1)
	4.438%
115000	= PMT * (((1-(1 + 4.438%) ^- 30)) / 4.35%)
115000	= PMT * 16.740
Annual Payment=	115000/16.740
Annual Payment=	6,870
So balance outstanding after 5 years	= 6870 * (((1-(1 + 4.438%) ^- 25)) / 4.35%)
So balance outstanding after 5 years	104,591.32