Question

Suppose you take out a 30-year mortgage for $169,221 at an annual interest rate of 3.8%. After 19 years, you refinance to an annual rate of 1.1%. How much interest did you pay on this loan?

Answer 1

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

C = Cash flow per period

i = interest rate

n = number of payments

169221= Cash Flow*((1-(1+ 3.8/1200)^(-30*12))/(3.8/1200))

Cash Flow = 788.5

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

C = Cash flow per period

i = interest rate

n = number of payments

PV= 788.5*((1-(1+ 3.8/1200)^(-11*12))/(3.8/1200))

PV = 84959.5

Interest paid in first 19 years = cash flow*months-(loan amount - PV after 19 years)

=788.5*12*19-(169221-84959.5)

=

95516.5

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

C = Cash flow per period

i = interest rate

n = number of payments

84959.5= Cash Flow*((1-(1+ 1.1/1200)^(-11*12))/(1.1/1200))

Cash Flow = 683.65

interest in last 11 years = CF*months-PV after 19 years

=683.65*12*11-84959.5

=

5282.3

Total interest = 5282.3+95516.5

=

100798.8