Answer:
2434.235983
356794.4755
14.5
Step-by-step explanation:
Let's start by finding the effective rate
.054/12= .0045
and then the payment
[tex]433500=x\frac{1-(1+.0045)^{-30*12}}{.0045}\\x=2434.235983[/tex]
There are two ways to find the unpaid balance (we also call this the oustanding loan balance). For this question (because all payments are equal) I am going to use the prospective method. The prospective method states that the outstanding loan balance is just the present value of the remaining payments
If 10 years have passed there are 20*12 payments and so we just need to find the present value of that
[tex]2434.235983*\frac{1-(1+.0045)^{-20*12}}{.0045}=356794.4755[/tex]
2.) We have the new loan amount (356794.4755) and so now we just need to calculate how long it will take it pay it off at a different rate
new effective rate: .024/12 = .002
[tex]356794.4755=2434.235983*\frac{1-(1+.002)^{-12x}}{.002}\\.70685301=1.002^{-12x}\\\log_{1.002}.70685301=-12x\\x=14.5[/tex]
