Question

A 25-year, $435,000 mortgage at 4.10% compounded quarterly is repaid with monthly payments.

a. What is the size of the monthly payments?

b. Find the balance of the mortgage at the end of 6 years?

c. By how much did the amortization period shorten by if the monthly payments are increased by $100 at the end of year six?

Answer 1

a

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

? = ((1+4,1/(4*100))^4-1)*100

Effective Annual Rate% = 4,1635

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

4,1635 = ((1+Stated rate%/(12*100))^12-1)*100

Stated rate% = 4,0861

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

C = Cash flow per period

i = interest rate

n = number of payments I f = frequency of payment

435000= Cash Flow*((1-(1+ 4,0861/1200)^(-25*12))/(4,0861/1200))

Cash Flow = 2316,82

Using Calculator: press buttons "2ND"+"FV" then assign

PV =-435000

I/Y =4,0861/12

N =25*12

FV = 0

CPT PMT

Using Excel

=PMT(rate,nper,pv,fv,type)

=PMT(4,0861/(12*100),12*25,,435000,)

b

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

C = Cash flow per period

i = interest rate

n = number of payments I f = frequency of payment

PV= 2316,82*((1-(1+ 4,0861/1200)^(-19*12))/(4,0861/1200))

PV = 366949,96

Using Calculator: press buttons "2ND"+"FV" then assign

PMT =2316,82

I/Y =4,0861/12

N =19*12

FV = 0

CPT PV

Using Excel

=PV(rate,nper,pmt,FV,type)

=PV(4,0861/(12*100),12*19,,PV,)

c

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

C = Cash flow per period

i = interest rate

n = number of payments I f = frequency of payment

366949,96= 2416,82*((1-(1+ 4,0861/1200)^(-n*12))/(4,0861/1200))

n(in years) = 17,84

Using Calculator: press buttons "2ND"+"FV" then assign

PV =-366949,96

PMT =2416,82

I/Y =4,0861/12

FV = 0

CPT N

Number of years = N/12

Using Excel

=NPER(rate,pmt,pv,fv,type)/no. of payments per year

=NPER(4,0861/(12*100),-2416,82,,366949,96,)/12

Decrease in time = 19-17.84 = 1.16 years