Question

How much interest (to the nearest dollar) would be saved on the following loan if the home were financed for 15 rather than 30 years? A $518,000 home bought with a 20% down payment and the balance financed for 30 years at 5.4%

Answer 1

Formula for Equal Annual payment:

Annual payment = (r x P)/ [1-(1+r)^-n]

P = Principal = $ 518,000 x 0.80 = $ 414,400

r = rate of interest = 5.4 %

n = No. of periods = 30

Annual payment = (0.054 x $ 414,400)/ [1-(1+0.054)^-30]

                             = $ 22,377.60/[1-(1.054)^-30]

                              = $ 22,377.60/ (1-0.206434211942536)

                              = $ 22,377.60/ 0.793565788057464

                              = $ 28,198.7962898163 or $ 28,198.80

Total amount to pay = Number of payments x Annual payment = 30 x $ 28,198.80 = $ 845,964

Total interest = Total amount to pay – Principal = $ 845,964 - $ 414,400 = $ 431,564

For 15 year loan:

Annual payment = (0.054 x $ 414,400)/ [1-(1+0.054)^-15]

                             = $ 22,377.60/[1-(1.054)^-15]

                              = $ 22,377.60/ (1- 0.454350318523643)

                              = $ 22,377.60/ 0.545649681476357

                              = $ 41,010.9283660777 or $ 41,010.93

Total amount to pay = Number of payments x Annual payment = 30 x $ 41,010.93 = $ 615,163.95

Total interest = Total amount to pay – Principal = $ 615,163.95 - $ 414,400 = $ 200,763.95

Difference in interest = $ 431,564 - $ 200,763.95 = $ 230,800.05 or $ 230,800

Interest of $ 230,800 would be saved on financing the loan for 15 years rather than 30 years.