In: Finance
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?
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