Question

Artemis took out a 30-year loan from her bank for $190,000 at an APR of

Answer 1

The prepayment fee of $6182.58 would  be charged to Artemis for paying off her loan 16 years early.

Answer: Option C

Step-by-step explanation:

30 year loan at 9.6% interest yields.  

Number of month = 30 (12) = 360 months

Annual percent interest of $\frac{9.6 \%}{12}$ = monthly percent interest of .8%

The formula for the present value of an ordinary annuity, as opposed to an annuity due, is as follows

            $P M T= \frac{P \times r}{1-(1+r)^{n}}$

With r and n adjusted for periodicity, where

P = the present value of an annuity stream

PMT = the dollar amount of each annuity payment

r = the interest rate (also known as the discount rate)

n = the number of periods in which payments will be made

              $P M T= \frac{190000 \times 0.008}{1-(1+0.008)^{-360}} = \frac{1520}{1-(1.008)^{-360}} = \frac{1520}{1-0.0567}=\frac{1520}{0.9432}$

                   PMT = $1611.50 per month

Her loan 16 year early. It means

              $\text { Worth of loan after } 14 \text { year } = 190000 \times(1.008)^{168} = 3.814 \times 190000=\ 724641.16$

Worth of monthly payments for 14 year

           $= \frac{1611.50 \times\left\{(1.008)^{168}-1\right)}{0.008} = \frac{1611.50 \times(3.81-1)}{0.008} = \frac{4.534 .6}{0.008} = \ 566825.15$

Amount still owed after 14 year = difference of the above two

                                                    =$724641.16 - $566825.18

                                                    =$157816.01

Prepayment fee = $(0.8 \times 157816.02) \times\left((1.008)^{6}-1\right)$

                         = 126252.82 (1.049-1) = 126252.82 (1.0489-1) = $6182.63

Answer 2

Answer: $6182.58  APEX