Question

Your firm has taken out a $ 530 000 loan with 8.6 % APR​ (compounded monthly) for some commercial property. As is common in commercial real​ estate, the loan is a 5​-year loan based on a 15​-year amortisation. This means that your loan payments will be calculated as if you will take 15 years to pay off the​ loan, but you actually must do so in 5 years. To do​ this, you will make 59 equal payments based on the 15​-year amortisation schedule and then make a final 60th payment to pay the remaining balance.  ​(Note: Be careful not to round any intermediate steps to fewer than six decimal​ places.) a. What will your monthly payments​ be? b. What will your final payment​ be? a. What will your monthly payments​ be? The monthly payments will be ​$ nothing. ​(Round to the nearest​ cent.) b. What will your final payment​ be? The final payment will be ​$ nothing. ​(Round to the nearest​ cent.)

Answer 1

We can find the monthly payment using present value of annuity formula.

Where,
PVA = Present Value of Annuity
A = Annuity or Payment
i = rate of interest
n = number of years
a = number of payments per year
na = total number of payments

We will find the monthly payment as if it is 15 year loan. Therefore, n = 15, a = 12 and i = 0.086

Substituting the values in the formula, we get:

So the monthly payment is $5250

We can use this amount to find the balance after 59th payment.

Here, PV is original balance or amount of loan and na = 59

Therefore, final payment is $423.846.51