Question

Raymond took out a 25-year loan for $135,000 at an APR of 3.6% compounded monthly. If his bank charges a prepayment fee of 6 months' interest on 80 % of the balance, what prepayment fee would he be charged for paying off the loan 5 years early?

Answer 1

Answer:543.46

Explanation:

Answer 2

Remaining balance would have been $37457.92

Explanation:

number of month, n = 25 × 12 = 300 months.

APR = 3.6% annually

= 0.3% monthly ( Divide the annual rate by 12)

Principal value = $135000

`\text{Monthly Payment = }(rate* principal)/(1-(1+rate)^(-n))\\\\\implies\text{Monthly Payment = }(0.003* 135000)/(1-(1+0.003)^(-300))\\\\\bf\implies\textbf{Monthly Payment = }\$683.10`

If he pay 683.10 every month for 240 months, the remaining balance on the loan is = 37,457.92

If you assume they are using monthly interest rate for 6 months, then the penalty assessed would be :

`37457.9176* (1 + (0.036)/(12)) ^ 6 = 38137.24 - 37457.92 = 679.32`

Since, the loan was originally scheduled to go 300 months, then paying off the loan by the end of month 240 would be 5 years early, because 5 years is equal to 60 months and 300 - 60 is equal to 240 months

The key component here is what would be the remaining balance after 240 months of paying the loan off at $683.10 every month.

That remaining balance would have been $37457.92