Question

Need help please show work

Answer 1

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

$433500=x\frac{1-(1+.0045)^{-30*12}}{.0045}\\x=2434.235983$

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

$2434.235983*\frac{1-(1+.0045)^{-20*12}}{.0045}=356794.4755$

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

$356794.4755=2434.235983*\frac{1-(1+.002)^{-12x}}{.002}\\.70685301=1.002^{-12x}\\\log_{1.002}.70685301=-12x\\x=14.5$

Answer 2

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

\begin{gathered}433500=x\frac{1-(1+.0045)^{-30*12}}{.0045}\\x=2434.235983\end{gathered}

433500=x

.0045

1−(1+.0045)

−30∗12

x=2434.235983

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

2434.235983*\frac{1-(1+.0045)^{-20*12}}{.0045}=356794.47552434.235983∗

.0045

1−(1+.0045)

−20∗12

=356794.4755

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

\begin{gathered}356794.4755=2434.235983*\frac{1-(1+.002)^{-12x}}{.002}\\.70685301=1.002^{-12x}\\\log_{1.002}.70685301=-12x\\x=14.5\end{gathered}

356794.4755=2434.235983∗

.002

1−(1+.002)

−12x

.70685301=1.002

−12x

log

1.002

.70685301=−12x

x=14.5