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 $504,000 home bought with a 20% down payment and the balance financed for 30 years at 5.9% $

Answer 1

Loan Amount = 504,000 × 80% = $403,200

Assumption: Loan is repayable in  EMI with interest compounded on monthy basis

EMI = P×r×(1+r)ⁿ/[(1+r)ⁿ-1]

Where, P = Principal = $403,200

r = Rate of Interest on monthly basis = 5.9/12 = 0.4917%

n = number of installments = 30 × 12 = 360 & 15 ×12 = 180

EMI (30 years) = 403,200 × 0.004917 × (1+0.004917)³⁶⁰/[(1+0.004917)³⁶⁰-1] = $2391.6296

EMI (15 years) = 403,200 × 0.004917 × (1+0.004917)¹⁸⁰/[(1+0.004917)¹⁸⁰-1] = $3380.7727

Interest Saved = Total Payment in 30 year tenor - Total Payment in 15 year tenor

     = (2391.6296×360) - (3380.7727×180)  = $252,447.57