Question

Consider a 30-year mortgage for $327,723 at an annual interest rate of 5.6%. After 12 years, the mortgage is refinanced to an annual interest rate of 3.3%. How much interest is paid on this mortgage? The answer is 282,628, but I'm not sure why?

Answer 1

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

C = Cash flow per period

i = interest rate

n = number of payments

327723= Cash Flow*((1-(1+ 5.6/1200)^(-30*12))/(5.6/1200))

Cash Flow = 1881.39

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

C = Cash flow per period

i = interest rate

n = number of payments

PV= 1881.39*((1-(1+ 5.6/1200)^(-18*12))/(5.6/1200))

PV = 255678.95

Interest paid in first 12 years = CF*months-(initial loan amount-PV after 12 years)

=1881.39*12*12-(327723-255678.95)

=

198876.11

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

C = Cash flow per period

i = interest rate

n = number of payments

255678.95= Cash Flow*((1-(1+ 3.3/1200)^(-18*12))/(3.3/1200))

Cash Flow = 1571.44

Interest paid in next 18 years = CF*months-PV after 12 years = 1571.44*18*12-255678.95

=

83752.09

Total interest = 83752.09+198876.11

=

282628