Your firm has taken out a loan with APR (compounded monthly) for some commercial property. As is common in commercial real estate, the loan is a -year loan based on a -year amortization. This means that your loan payments will be calculated as if you will take years to pay off the loan, but you actually must do so in years. To do this, you will make equal payments based on the -year amortization schedule and then make a final 60th payment to pay the remaining balance. A. What will your monthly payments be?
B. What will your final payment be?

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Your firm has taken out a $500000 loan with 9% APR (compounded monthly) for some commercial property. As is common in commercial real estate, the loan is a five-year loan based on a 15-year amortization. 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 five years. To do this, you will make 59 equal payments based on the 15 -year amortization schedule and then make a final 60th payment to pay the remaining balance.

answer : A) $5071.33

              B ) $405410.94

Explanation:

A )calculate monthly payments

Loan amount = $500000

Rate = 9%

Monthly rate =  ( 9% / 12 )= 0.75%

Time / period = (15years* 12 ) = 180 months

calculate the monthly payments =PMT (monthly rate ,period - rate) ( using excel )

= $5071.33

B) Calculate the final payment

PV for 59 payments + PV for 60th payment = loan amount

first we calculate the PV for 59 payments

monthly payments = $5071.33

period = 59 months

monthly rate = 0.75%

PV for 59 payments = PMT( monthly rate, period, - monthly payments ) (using excel )  

= $241,064.16

Hence PV for The final payment = loan amount - PV for 59 payments

                                                     = 500000 - 241064.16 = $258,935.84

Finally Calculate the Final payment

PV = $258935.84

monthly rate = 0.75%

period = 60 months

Final payment ( future value ) =FV( monthly rate, period,, - PV ) ( using excel)

= $405410.94

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