Question

Your firm has taken out a $ 544 comma 000$544,000 loan with 8.4 %8.4% APR​ (compounded monthly) for some commercial property. As is common in commercial real​ estate, the loan is a 55​-year loan based on a 1515​-year amortization. This means that your loan payments will be calculated as if you will take 1515 years to pay off the​ loan, but you actually must do so in 55 years. To do​ this, you will make 5959 equal payments based on the 1515​-year amortization schedule and then make a final 60th payment to pay the remaining balance.  ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.) a. What will your monthly payments​ be? b. What will your final payment​ be?

Answer 1

First, we need to find the equal monthly payment on the loan ,

using the Present Value of ordinary (month-end) annuity formula,

PV of Loan=Pmt.*(1-(1+r)^-n)/r

where,

PV of loan= 544000 (given)

Pmt.=the equal mthly. Pmt. To be found out--??

r= 8.4% p.a..ie. 8.4%/12= 0.70 % or 0.007 p.m

n= no.of payment periods= 15*12= 180 mths.

So, plugging in the values, in the formula,

544000=Mthy pmt.*(1-1.007^-180)/0.007

Solving the above, we get the mthy.pmt. As

544000/((1-1.007^-180)/0.007)=

5325.14

Next, we need to find the Loan Principal balance(FV) at the end of 59th payment

ie.FV at end 59 th mth= FV of the original loan-FV of the mthly . Annuities (both at end 59 th pmt.)

ie.FV at end 59 th mth=( PV*(1+r)^n)-(Mthly.pmt.*((1+r)^n-1)/r))

here,

FV of the loan balance ---is to be found out ---??

PV= the present value of Loan= 544000

r= mthly. Int. rate=0.007

n=no.of pmts.= 59

Mthly .pmt.= 5325.14 (as found out above)

So, plugging in all the values,

FV at end 59 th mth=(544000*(1+0.007)^59)-(5325.14*((1+0.007)^59-1)/0.007))=

433644.95

So the ANSWERS will be

a.Monthly payments​= $ 5325.14   &

b. The final payment will ​ be = $ 433644.95

ie.

a.   $ 5325

b. $ 433645