Question

Andy takes out a fully amortized 30 year loan at 5.9% for his $350,000 house (No down payment). 15 years later, he wins the lottery and decides to pay off his house immediately. How much interest did he save by not holding onto the loan for the full 30 years assuming no early payment penalty? Can solve using the simple finance functions on calculator.

Answer 1

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

C = Cash flow per period

i = interest rate

n = number of payments

350000= Cash Flow*((1-(1+ 5.9/1200)^(-30*12))/(5.9/1200))

Cash Flow = 2075.98

Principal remaining after 15 years

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

C = Cash flow per period

i = interest rate

n = number of payments

PV= 2075.98*((1-(1+ 5.9/1200)^(-15*12))/(5.9/1200))

PV = 247593.29

Interest saved = number of payments remaining*payment amount-principal remaining

=12*15*2075.98-247593.29=126083.11