Q:

Melanie took out a 20-year loan for $50,000 at an APR of 3.3%, compoundedmonthly. Approximately how much would she save if she paid it off 6 yearsearly?

Accepted Solution

A:
Answer:She would save $17,340.10.Step-by-step explanation:We will use formula : [tex]A=P(1+r)^t[/tex]A = Future amountP = Principal amountr = [tex]\frac{APR}{12}[/tex] =  [tex]\frac{0.033}{12}[/tex] = 0.00275t = 20 years ( 240 months )[tex]A=50,000(1+0.00275)^{240}[/tex]   = 50,000(1.00275)²⁴⁰   = 50,000 × 1.93304052   = $96,652.026 ≈ $96,652.03If she paid it off 6 years early ( after 14 years ).[tex]A=50,000(1+0.00275)^{168}[/tex] [tex]=50,000(1.00275)^{168}[/tex]  = 50,000 × 1.58623917  = 79,311.9585 ≈ $79,311.96She would save by paying off 6 years early = 96,652.03 - 79,311.96                                                                         = $17,340.07 ≈ 17,340.10She would save $17,340.10.