Answer:
$74,703.02
Step-by-step explanation:
You want the amount of interest saved by refinancing a 30 year loan of $160198 less 20% at an interest rate of 9.3% after 10 years to a 20 year loan at 4.8%.
The amount originally financed was ...
$160,198 × (1 -20%) = $128,158.40
The remaining balance after n of N monthly payments on a loan of P at interest rate r is given by the formula ...
[tex]B=P\left(1-\dfrac{(1+r/12)^n-1}{(1+r/12)^N-1}\right)\\\\\\B=128158.40\left(1-\dfrac{(1+.093/12)^{120}-1}{(1+.093/12)^{360}-1}\right)\approx115217.39[/tex]
The interest paid on a loan of P at rate r in N monthly payments is given by this formula. The interest on the remaining balance at the different interest rates will be ...
[tex]I=P\left(\dfrac{N(r/12)}{1-(1+r/12)^{-N}}-1\right)\\\\\\I=115217.39\left(\dfrac{240(.0075)}{1-1.0075^{-240}}-1\right)\approx138936.48\quad\text{1st loan interest}\\\\\\I=115217.39\left(\dfrac{240(.004)}{1-1.004^{-240}}-1\right)\approx64233.46\quad\text{2nd loan interest}[/tex]
The amount of interest saved by financing at the lower rate is ...
$138936.48 -64233.46 = $74703.02
Refinancing saves $74703.02 in interest.
