Question

House Appreciation and Mortgage Payments
Say that you purchase a house for $400,000 by getting a mortgage for $320,000 and paying a $80,000 down payment.
A. If you get a 20-year mortgage with a 4 percent interest rate, what are the monthly payments?
B. What would the loan balance be in ten years?
C. If the house appreciates at 6 percent per year, what will be the value of the house in ten years?
D. How much equity do you have in the house after ten years?
E. How much is the house worth after twenty years, when the mortgage is paid off?

Answer 1

A

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

320000= Cash Flow*((1-(1+ 4/1200)^(-20*12))/(4/1200))

Cash Flow = 1939.14

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

PV =-320000

I/Y =4/12

N =20*12

FV = 0

CPT PMT

Using Excel

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

=PMT(4/(12*100),12*20,,320000,)

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= 1939.14*((1-(1+ 4/1200)^(-10*12))/(4/1200))

PV = 191529.2

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

PMT =1939.14

I/Y =4/12

N =10*12

FV = 0

CPT PV

Using Excel

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

=PV(4/(12*100),12*10,,PV,)

C

Future value = present value*(1+ rate)^time

Future value = 400000*(1+0.04)^10

Future value = 592097.71

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

PV =-400000

I/Y =4

N =10

PMT = 0

CPT FV

Using Excel

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

=FV(0.04,10,,-400000,)

D

Equity = FV-loan outstanding = 592097.71-191529.2

=

400568.51

E

Future value = present value*(1+ rate)^time

Future value = 400000*(1+0.06)^20

Future value = 1282854.19

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

PV =-400000

I/Y =6

N =20

PMT = 0

CPT FV

Using Excel

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

=FV(0.06,20,,-400000,)