Question

How much interest (to the nearest dollar) would be saved on the following loan if the condominium were financed for 15 rather than 30 years? A $251,000 condominium bought with a 30% down payment and the balance financed for 30 years at 3.05%

Answer 1

The formula used to calculate the fixed monthly payment (P) required to fully amortize a loan of $ L over a term of n periods at an interest rate of r per period is

P = L[r(1 + r)ⁿ]/[(1 + r)ⁿ - 1].

here L = $ 251,000 – 30 % of $ 251,000 = $ 175700, r = 3.05 % = 3.05/100 = 0.0305 and n = 30 so that P = 175700*0.0305[(1+0.0305)³⁰]/ [(1+0.0305)³⁰ -1] = 175700*0.0305*2.462860897/1.462860897 = $ 9022.12 ( on rounding off to the nearest cent). Thus, the loan of $ 175700 would be fully paid off, with interest , by 30 annual instalments of $ 9022.12 each. Therefore, the amount of interest paid in 30 years is 30*$ 9022.12 -$ 175700 = $ (270663.60-175700) = $ 94963.60.

If the loan of $ 175700 is paid off in 15 years, then P = 175700*0.0305*(1.0303)¹⁵/[(1.0303)¹⁵ -1] = 175700*0.0305*1.56935047/0.56935047 = 14771.07 ( on rounding off to the nearest cent).

Thus, the loan of $ 175700 would be fully paid off, with interest , by 15 annual instalments of $ 14771.07 each. Therefore, the amount of interest paid in 15 years is 30*$ 14771.07-$ 175700 = $ (221566.05-175700) = $ 45866.05.

Hence, the saving in interest if the condominium were financed for 15 rather than 30 years is $ 94963.60 -$ 45866.05 = $ 49097.25.