You have just arranged for a $1,620,000 mortgage to finance the purchase of a large tract of land. The

You have just arranged for a $1,620,000 mortgage to finance the purchase of a large tract of land. The mortgage has an APR of 6.2 percent, and it calls for monthly payments over the next 22 years. However, the loan has an eight-year balloon payment, meaning that the loan must be paid off then.

 

How big will the balloon payment be? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

 

Balloon payment

$

Explanation:

The monthly payments with a balloon payment loan are calculated assuming a longer amortization schedule, in this case, 22 years. The payments based on a 22-year repayment schedule would be:

  

PVA = $1,620,000 = C({1 – [1 / (1 + 0.062/12)264]} / (0.062/12))

C = $11,258.10

  

Now, at Time = 8, we need to find the PV of the payments which have not been made. The balloon payment will be:

  

PVA = $11,258.10({1 – [1 / (1 + 0.062/12)12(14)]} / (0.062/12))

PVA = $1,262,223.38

   

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

Enter

22 × 12

6.2% / 12

$1,620,000

N

I/Y

PV

PMT

FV

Solve for

$11,258.10

   

Enter

14 × 12

6.2% / 12

$11,258.10

N

I/Y

PV

PMT

FV

Solve for

$1,262,223.38