Question

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

9.6%, compounded monthly. If her bank charges a prepayment fee of 6
months' interest on 80% of the balance, what prepayment fee would Artemis
be charged for paying off her loan 16 years early?
O
A. $5822.42
O
B. $7390.60
O C. $6182.58
O D. $7382.56

Answer 1

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

Answer: Option C

Explanation:

30 year loan at 9.6% interest yields.

Number of month = 30 (12) = 360 months

Annual percent interest of
`(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= (P * 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= (190000 * 0.008)/(1-(1+0.008)^(-360)) = (1520)/(1-(1.008)^(-360)) = (1520)/(1-0.0567)=(1520)/(0.9432)`

PMT = $1611.50 per month

Her loan 16 year early. It means

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

Worth of monthly payments for 14 year

`= \frac{1611.50 *\left\{(1.008)^(168)-1\right)}{0.008} = (1611.50 *(3.81-1))/(0.008) = (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 * 157816.02) *\left((1.008)^(6)-1\right)`

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