Question

Apollo took out a 30-year loan from his bank for $180,000 at an APR of 8.4%, compounded monthly. If his bank charges a prepayment fee of 6 months' interest on 80% of the balance, what prepayment fee would Apollo be charged for paying off his loan 14 years early? A) $4623.49 B) $4943.37 C) $6099.06 D) $6090.63 PLEASE HELP

Answer 1

Hi there
First find the monthly payment of this loan by using the formula of the present value of annuity ordinary
The formula is
Pv=pmt [(1-(1+r/k)^(-kn))÷(r/k)]
Pv present value 180000
PMT monthly payment?
R interest rate 0.084
K compounded monthly 12
N time 30 years
We need to solve for pmt
PMT=pv÷ [(1-(1+r/k)^(-kn))÷(r/k)]
PMT=180,000÷((1−(1+0.084÷12)^(
−12×30))÷(0.084÷12))
=1,371.3077854899

Second find The amount owed using the same formula
Pv=pmt [(1-(1+r/k)^(-kn))÷(r/k)]
Pv amount owed?
PMT 1,371.3077854899
R 0.084
K compounded monthly 12
N 14 years
Pv=1,371.3077854899×((1−(1+0.084÷12)^(−12×14))
÷(0.084÷12))=135,215.48447736

80% of the balance135,215.48447736

135,215.48447736×0.8
=108,172.38758189

Prepayment fee
108,172.38758189×((1+0.084÷12)^(6)−1)
=4,623.49...answer

It's a

Good luck!