Question

A 25-year, $455,000 mortgage at 4.30% compounded semi-annually 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 $275 at the end of year six?

Answer 1

a

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

? = ((1+4,3/(2*100))^2-1)*100

Effective Annual Rate% = 4,3462

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

4,3462 = ((1+Stated rate%/(12*100))^12-1)*100

Stated rate% = 4,262

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

455000= Cash Flow*((1-(1+ 4,262/1200)^(-25*12))/(4,262/1200))

Cash Flow = 2467,97

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

PV =-455000

I/Y =4,262/12

N =25*12

FV = 0

CPT PMT

Using Excel

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

=PMT(4,262/(12*100),12*25,,455000,)

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= 2467,97*((1-(1+ 4,262/1200)^(-19*12))/(4,262/1200))

PV = 385243,22

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

PMT =2467,97

I/Y =4,262/12

N =19*12

FV = 0

CPT PV

Using Excel

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

=PV(4,262/(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

385243,22= 2742,97*((1-(1+ 4,262/1200)^(-n*12))/(4,262/1200))

n(in years) = 16,24

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

PV =-385243,22

PMT =2742,97

I/Y =4,262/12

FV = 0

CPT N

Number of years = N/12

Using Excel

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

=NPER(4,262/(12*100),-2742,97,,385243,22,)/12

Reduction in years = 19-16.24=2.76 years